Probability Questions

We provide probability practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on probability skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Probability Questions

List of probability Questions

Question NoQuestionsClass
1Probability of an impossible event is12
2Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( boldsymbol{P}(overline{boldsymbol{A}} cap overline{boldsymbol{B}}) )
12
3In a binomial distribution mean is 4.8
and variance is ( 2.88, ) then the
parameter ( n ) is
A . 8
B. 12
c. 16
D. 20
12
4Once you toss a coin, you will get the result as head or tail. Doing this action is called an
A . space
B. sample
c. experiment
D. event
12
57.
The probability that A speaks truth is 5while the
probability for
The probability that they contradict
20041
each other when asked to speak on a fact is
111it distribution.
12
6If ( S ) is a sample space ( P(A)=frac{1}{3} P(B) )
and ( S=A cup B ) where ( A ) and ( B ) are two
mutually exclusive events, then
( boldsymbol{P}(boldsymbol{A})= )
A ( cdot frac{1}{4} )
в. ( frac{1}{2} )
( c cdot frac{3}{4} )
D.
12
7The probability of ( A= ) Probability of ( B= ) Probability of ( mathrm{C}=frac{1}{4} )
( boldsymbol{P}(boldsymbol{A}) cap boldsymbol{P}(boldsymbol{B}) cap boldsymbol{P}(boldsymbol{C})=mathbf{0} . boldsymbol{P}(boldsymbol{B} cap boldsymbol{C})= )
0 and ( P(A cap C)=frac{1}{8} . P(A cap B)=0 ) the
probability that atleast one of the events ( A, B, C ) exists is?
A ( cdot frac{5}{8} )
в. ( frac{37}{64} )
( c cdot frac{3}{4} )
( D )
12
818.
If three distinct numbers are chosen randomly from the
first 100 natural numbers, then the probability that all three
of them are divisible by both 2 and 3 is
(2004S)
(a) 4/25 (b) 4/35 (c) 4/33 (d) 4/1155
11
9State and prove Addition theorem on
probability.
12
10B
uch that P(AUB)=3/4, P(
A
A and B are events such that P(AUB)=3/4,
P(A)=2/3 then PA B ) is
(a) 5/12 (b) 3/8 (c) 5/8 (d)
)=1/4,
[2002]
1/4
A di
dered
11
11Which of the following cannot be the probability of an event?
A ( cdot frac{2}{3} )
в. -1.5
c. ( 15 % )
D. 0.7
12
12( A ) box ( B_{1} ) contains 1 white ball, 3 red
balls and 2 black balls. Another box ( B_{2} )
contains 2 white balls, 3 red balls and 4
black balls. A third box ( B_{3} ) contains 3
white balls, 4 red balls and 5 black balls If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that
these 2 balls are drawn from box ( B_{2} ) is
A ( cdot frac{116}{181} )
в. ( frac{126}{181} )
c. ( frac{65}{181} )
D. ( frac{55}{181} )
12
13From a batch of 100 items of which 20
are defective, exactly two items are chosen, one at a time, without
replacement. Calculate the probabilities that the second item chosen is defective
A ( cdot frac{2}{5} )
в. ( frac{19}{100} )
( c cdot frac{1}{5} )
D. none of these
12
14A card is drawn at random from a well
shuffled card. find the probability of card drawn is a black king.
A ( cdot frac{1}{26} )
B. ( frac{2}{26} )
c. ( frac{4}{26} )
D. None of the above
12
158.
One hundred identical coins, each with probability, p, of
showing up heads are tossed once. If 0 < p < 1 and the
probabilitity of heads showing on 50 coins is equal to that
of heads showing on 51 coins, then the value of p is
(1988 – 2 Marks)
(a) 1/2 (b) 49/101 (c) 50/101 (d) 51/101.
1
12
16The binomial distribution whose mean
is 9 and the variance is 2.25 is
( ^{mathbf{A}} cdotleft(12, frac{1}{2}, frac{1}{2}right) )
B ( cdotleft(12, frac{2}{3}, frac{1}{3}right) )
( ^{mathbf{c}} cdotleft(12, frac{5}{6}, frac{1}{6}right) )
D. ( left(12, frac{3}{4}, frac{1}{4}right) )
12
17A die has 6 faces marked by the given numbers as shown below:
The die is thrown once. What is the
probability of getting an integer greater
than ( -mathbf{3} ? )
( 1 3 longdiv { 2 3 } )
12
18How many outcomes are possible when a coin is tossed
A. 2 times
B. 3 times
c. 4 times
D. 5 times
12
19A salesman has a ( 70 % ) chance to sell a
product to any customer. The behaviour of successive customers is independent. If two customers ( A ) and ( B ) enter, what is the probability that the salesman will sell the product to
customer A or B?
A . 0.98
B. 0.91
c. 0.70
D. 0.49
12
20In how many different ways can the letter of the word FINANCE be arranged?
A . 5040
в. 2040
( c .2520 )
D. 4080
E. None of these
12
21In a test an examine either gusses or copies or knows the answer to a
multiple choice question with ( m ) choices out of which exactly one is correct. The probability that he makes a guess is ( 1 / 3 ) and the probability that he copies the answer is 1/6. The probability that his answer is correct given that the copied it, is ( 1 / 8 . ) If the probability that he knew the answer to the question given that he correctly answered it is ( 120 / 141 )
find ( boldsymbol{m} )
12
22There are two coins, one unbiased with probability ( frac{1}{2} ) of getting heads and the other one is biased with probability ( frac{3}{4} ) of getting heads. A coin is selected at random and tossed. It shows heads up.
Then the probability that the
unbiasedcoin was selected is
A ( cdot frac{2}{3} )
в. ( frac{3}{5} )
c. ( frac{1}{2} )
D. ( frac{2}{5} )
12
23In a certain population ( 10 % ) of the people are rich, ( 5 % ) are famous and ( 3 % ) are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to
A . 0.07
B. 0.08
c. 0.09
D. 0.12
12
24A die is thrown. Write the sample space.
If ( A ) is the event that the number is a
perfect square, write the event ( boldsymbol{A} ) using set notation.
12
25For three events ( A, B ) and ( C, P( ) exactly
one of the events ( A text { or } B text { occurs })=P( )
exactly one of the vents ( B ) or ( C ) occurs
( =P(text { exactly one of the events } C text { or } A ) occurs ( )=p ) and ( P( ) all the three events
occur simultaneously ( )=p^{2}, ) where ( 0< )
( boldsymbol{p}<frac{1}{2} )
Then the probability of atleast one of the three events ( A, B ) and ( C ) occurring is
A ( cdot frac{3 p+2 p^{2}}{2} )
в. ( frac{p+3 p^{2}}{2} )
c. ( frac{3 p+p^{2}}{2} )
D. ( frac{3 p+2 p^{2}}{4} )
12
26Three numbers are chosen at random
from the first 20 natural numbers. Then
what is the probability that their product is odd?
12
27If ( boldsymbol{P}(boldsymbol{A})=frac{1}{2}, boldsymbol{P}(boldsymbol{B})=0, ) then ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) )
is
( mathbf{A} cdot mathbf{0} )
B.
c. Not defined
D.
12
28The probability that a two digit number selected at random will be a multiple of
‘3’ and not a multiple of ‘5’ is
A ( cdot frac{2}{15} )
в. ( frac{4}{15} )
c. ( frac{1}{15} )
D. ( frac{4}{90} )
12
29Given two independent events ( A ) and ( B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} )
Find
(i) ( P(A text { and not } B) )
(ii) P(neither A nor
B)
12
30If two numbers ( p ) and ( q ) are chosen
randomly from the set {1,2,3,4} with replacement, then the probability that ( p^{2} leq 4 q ) is equal to
A ( cdot frac{1}{4} )
B. ( frac{3}{16} )
( c cdot frac{1}{2} )
D. ( frac{9}{16} )
E. ( frac{7}{16} )
12
31sleep. He classifies sleep activity in four stages: 1,2,3 and ( 4 . ) Stage 3 is the only stage considered to be deep sleep. Ajay goes to clinic for sleeping brainwashes analyzed. Doctor
monitored the person’s brainwashes in ( 15- ) minute intervals, for 8 continuous
hours, and categorized them into one of the four stages. The graph above shows this study. fone ( 15- ) minute time period is chosen at random, then the probability that the patient was in deep sleep during that time is ( frac{a}{b}, ) where ( a, b ) are co-primes. What is the value of ( a+b ? )
12
32A machine has three parts, ( A, B ) and ( C )
whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the
probability that the machine will not stop working?
A . 0.06
B. 0.16
c. 0.84
D. 0.94
12
33If ( A ) is required event and ( S ) is the
sample space, ( boldsymbol{n}(boldsymbol{A})=mathbf{3}, boldsymbol{n}(boldsymbol{S})=mathbf{6} )
then find ( boldsymbol{P}(boldsymbol{A}) )
12
34The probability that an automobile will be stolen and found within one week is
( 0.0006 . ) The probability that an
automobile will be stolen is ( 0.0015 . ) The
probability that a stolen automobile will be found in one week is
A . 0.3
B. 0.4
( c .0 .5 )
D. 0.6
12
35Two symmetrical dice are thrown at a time. If the sum of points on them is 7 the chance that one of them will show a
face with 2 points is
A ( cdot frac{1}{8} )
в. ( frac{1}{3} )
( c cdot frac{2}{3} )
D.
12
36When a die is thrown, list the outcomes
of an event of getting a prime number.
A ( cdot{1,4,6} )
в. {2,3,5}
D. None of these
12
37If the probability distribution of a random variable x is
( boldsymbol{X}=boldsymbol{x}_{1}: quad-2 quad-1 quad mathbf{0} quad mathbf{1} quad mathbf{2} quad mathbf{3} )
( boldsymbol{p}left(boldsymbol{X}=boldsymbol{x}_{1}right): mathbf{0 . 1} quad boldsymbol{k} quad mathbf{0 . 2} quad mathbf{2 k} mathbf{0 . 3} boldsymbol{k} )
then the mean of ( x ) is
A . 0.6
B. 0.8
( c .1 .0 )
D. 0.3
12
38Determine the binomial distribution
whose mean is 4 and variance 3
12
39In a hand at whist find the chance that a
specified player holds both the king and queen of trumps.

Note:Whist is a game of cards in which a standard pack of 52 cards is used.The game is played in pairs.In each round, a suit is randomly selected as ‘Trump’ which gets a preference over other suits for that particular round.

12
40Three coins are tossed. Describe
two events ( A ) and ( B ) which are mutually
exclusive.
12
41A card is down & replaced in ordinary pack of 52 playing cards. Minimum number of times must a card be drawn
so that there is atleast an even chance
of drawing a heart, is
A . 2
B. 3
( c cdot 4 )
D. more than four
12
42Consider two events ( A, B ) of an
zperiment satisfying ( boldsymbol{P}(boldsymbol{A} cup overline{boldsymbol{B}})=frac{mathbf{3}}{boldsymbol{4}} boldsymbol{&} )
( P(B)=frac{1}{2}, ) then ( Pleft(frac{A}{B}right) ) is equal to
A ( cdot frac{1}{3} )
B. ( frac{1}{4} )
( c cdot frac{1}{2} )
D.
12
43A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from
each bag, then the probability that one ball is white and one ball is black is
A ( cdot frac{5}{24} )
в. ( frac{13}{24} )
( c cdot frac{1}{4} )
D. ( frac{2}{3} )
12
44Two coins are tossed. Find the
probability, if ( boldsymbol{P} ) is the event of getting
two head
12
45A coin is tossed and a single 6 -sided die is rolled. Find the probability of landing on the tail side of the coin and rolling 4
on the die.
A ( cdot frac{1}{12} )
в. ( frac{6}{5} )
( c cdot frac{4}{3} )
D. ( frac{3}{4} )
12
46( A ) and ( B ) are events with ( P(A)=0.5, P(B)= )
0.4 and ( P(A cap B)=0.3 . ) Find the
probability that:
(i) A does not occur
(ii) Neither ( A ) and nor ( B ) occurs
12
47A bag contains 5 red, 6 white and 7
black balls. Two balls are drawn at
random. What is the probability that both balls are red or both are black?
A ( cdot frac{31}{153} )
в. ( frac{30}{153} )
c. ( frac{33}{153} )
D. ( frac{32}{153} )
12
48Let ( A ) and ( B ) be two events such that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) . ) Then
Statement ( 1: P(A cap bar{B})=P(bar{A} cap B)= )
0
Statement 2: If ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})=mathbf{1} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
49Two coins are tossed. What is the
conditional probability that two heads result, given that there is at least one head?
A ( cdot frac{1}{4} )
в. ( frac{2}{3} )
( c cdot frac{1}{3} )
D. ( frac{3}{4} )
12
50A factory produces bulbs. The probability that one bulb is defective is ( frac{1}{50} ) and they are packed in boxes of ( 10 . ) If the probability that none of the bulbs is defective from a single box is ( left(frac{49}{50}right)^{k} ) then value of ( k ) is12
51Let ( X ) and ( Y ) be two random variables.
The relationship ( boldsymbol{E}(boldsymbol{X} boldsymbol{Y})=boldsymbol{E}(boldsymbol{x}) cdot(boldsymbol{Y}) )
holds.
A. Always
B. If ( E(X+Y)=E(X)+E(Y) ) is true
c. If ( X ) and ( Y ) are independent
D. If ( X ) can be obtained from ( Y ) by a linear transformation
12
52( A ) and ( B ) each throw a die. The probability that ( A^{prime} ) ‘s throw is not greater than B’s is
A ( cdot frac{21}{36} )
в. ( frac{12}{35} )
c. ( frac{7}{12} )
D. ( frac{5}{12} )
12
53If a random variable ( X ) follows binomial
distribution with mean 3 and variance ( frac{3}{2}, ) and ( P(X leq 5)=frac{63}{2^{x}}, ) then the value
of ( ^{prime} x^{prime} ) is
12
54Suppose ( boldsymbol{E}_{1}, boldsymbol{E}_{2}, boldsymbol{E}_{3} ) be three mutually
exclusive events such that ( boldsymbol{P}left(boldsymbol{E}_{i}right)=boldsymbol{p}_{i} )
for ( boldsymbol{i}=mathbf{1}, mathbf{2}, mathbf{3} )
( operatorname{then} Pleft(E_{1} cap E_{2}^{prime}right)+Pleft(E_{2} cap E_{3}^{prime}right)+ )
( boldsymbol{P}left(boldsymbol{E}_{3} cap boldsymbol{E}_{1}^{prime}right) ) equals
A ( cdot p_{1}left(1-p_{2}right)+p_{2}left(1-p_{3}right)+p_{3}left(1-p_{1}right) )
В. ( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} )
c. ( p_{1}+p_{2}+p_{3} )
D. None of these
12
55Three integers are chosen at random without replacement from the 1st 20 integers. The probability that their
product is even is
A ( cdot frac{16}{19} )
в. ( frac{17}{19} )
c. ( frac{18}{19} )
D. ( frac{15}{19} )
12
56If ( C ) and ( D ) are two events such that
( mathbf{C} subset mathbf{D} ) and ( mathbf{P}(mathbf{D}) neq mathbf{0}, ) then the correct
statement among the following is
( ^{mathbf{A}} cdot pleft(frac{C}{D}right)=mathrm{P}(mathrm{C}) )
( ^{mathbf{B}} cdot pleft(frac{C}{D}right) geq mathrm{P}(mathrm{C}) )
( ^{c} cdot pleft(frac{C}{D}right)<mathrm{P}(mathrm{C}) )
( Pleft(frac{C}{D}right)=frac{P(D)}{P(C)} )
12
57Out of 800 families with 4 children
each, the expected number of families having atleast one boy is
A . 550
B. 50
c. 750
D. 300
12
58A card is drawn from a well-shuffled
deck of playing cards. Find the probability of drawing a face card.
( A cdot frac{8}{13} )
в. ( frac{3}{13} )
c. ( frac{4}{13} )
D. ( frac{1}{4} )
12
59Probability of any event ( boldsymbol{x} ) lies
A. ( 0<x<1 )
в. ( 0 leq x<1 )
c. ( 0 leq x leq 1 )
D. ( 1<x<2 )
12
60There are three coins. One is a two-
headed coin (having head on both faces), another is a biased coin that
comes up heads ( 75 % ) of the times and
third is also a biased coin that comes
up tails ( 40 % ) of the times. One of the three coins is chosen at random and
tossed, and it shows heads. What is the probability that it was the two-headed
( operatorname{coin} ? )
12
61In a class, there are 18 girls and 16 boys. The class teacher wants to choose
one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What
is the probability that the name written on the card is:
(i) the name of a girl
(ii) the name of a
boy
12
62For the events ( boldsymbol{A} ) and ( boldsymbol{B}, boldsymbol{P}(boldsymbol{A})= )
( frac{3}{4}, P(B)=frac{1}{5}, P(A cap B)=frac{1}{20} ) then
( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})= )
( A cdot frac{1}{4} )
B. ( frac{1}{15} )
( c cdot frac{3}{4} )
D.
12
63Red on first draw and white on second
draw
12
64A number ( x ) is selected at random from
the numbers 1,4,9,16 and another
number ( y ) is selected at random from
the number ( 1,2,3,4 . ) Find the
probability that the value of ( x y ) is more
than 16
12
65A student appears for tests, I, II and III The student is successful if he passes in
tests I, Il or I, Ill. The probabilities of the student passing in tests I, II and III are espectively ( mathrm{p}, mathrm{q} ) and ( frac{1}{2} . ) If the probability of the student to be successful is ( frac{1}{2} ) then
A ( cdot p(1+q)=1 )
B. ( q(1+p)=1 )
c. ( p q=1 )
D. ( frac{1}{p}+frac{1}{q}=1 )
12
66( A, B, C ) are three events for which
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{C})= )
( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 3} )
and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 2 .} ) If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup )
( C) geq 0.85 ) then the interval of values of
( boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is
В. [0.55,0.7]
D. none of these
12
67In an examination, the probability of a candidate solving a question is ( frac{1}{2} . ) Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2
questions?
A ( cdot frac{1}{64} )
в. ( frac{3}{16} )
( c cdot frac{1}{2} )
D. ( frac{13}{16} )
12
68If ( P(A)=P(B), ) then
( A cdot A ) and ( B ) are the same events
B. ( A ) and ( B ) must be same events
C. ( A ) and ( B ) may be different events
D. A and B are mutually exclusive events.
12
69A boy has a collection of blue and green marbles. The number of blue marbles
belong to the sets ( 2,3,4,13 . ) If two marbles are chosen simultaneously and at random from his collection, then the
probability that they have different colour is ( 1 / 2 . ) Possible number of blue marbles is:
A . 2
B. 3
( c cdot 6 )
D. 10
12
70n different toys are to be distributed among n children. Find the number of
ways in which these toys can be distributed so that exactly one child
gets no toy
12
71A letter is known to have come either
from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or ( boldsymbol{C A L} boldsymbol{C U T T A} )
On the envelope just two consecutive
letters ( T A ) are visible. What is the
probability that the letter came from
CALCUTTA?
( A cdot frac{4}{11} )
B. ( frac{7}{11} )
( c cdot frac{2}{11} )
D. None of these
12
72A die is thrown once. If ( A ) is the event
“the number appearing is a multiple of
( 3 ” ) and ( B ) is the event “the number
appearing is even” Are the event A and B independent?
12
73Let ( X ) denote the number of time tail
appear in ( n ) tosses of a fair coin. If
( boldsymbol{P}(boldsymbol{X}=mathbf{1}), boldsymbol{P}(boldsymbol{X}=mathbf{2}) ) and
( boldsymbol{P}(boldsymbol{X}=mathbf{3}) ) are in A.P., then value of ( boldsymbol{n} ) is
( mathbf{A} cdot mathbf{9} )
B . 2
( c cdot 7 )
D. None of these
12
74The probability of selecting a rotten apple randomly from a heap of 900 apples is ( 0.18 . ) What is the number of rotten apples in the heap?12
75Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3 2} )
12
76In an entrance test is graded on the basis of two examinations, the
probability of a randomly chosen
student passing the first examination
is 0.8 and the probability of passing the second examination is 0.7 . The
probability of passing at least of them is ( 0.95 . ) What is the probability of passing both?
12
77Twelve players ( S_{1}, S_{2}, dots, S_{12} ) play in a chess tournament. They are divided into
six pairs at random. From each pair a winner is decided. It is assumed that all
players are of equal strength. The probability that exactly one of ( S_{1} ) and ( S_{2} ) is among the six winners is
A ( cdot frac{6}{11} )
в. ( frac{5}{11} )
c. ( frac{4}{11} )
D. None of these
12
78The variance of the random variable ( x )
whose probability distribution is given by
( boldsymbol{X}=boldsymbol{x}_{i}: quad-1 quad, boldsymbol{0}, quad+1 )
( boldsymbol{p}left(boldsymbol{X}=boldsymbol{x}_{i}right): mathbf{0 . 4}, mathbf{0 . 2}, quad mathbf{0 . 4} ) is
A . 0.4
B. 0.6
( c .0 .8 )
D. 1.0
12
79Let ( A ) be a set containing ( n ) elements. ( A ) subset ( P ) of the set ( A ) is chosen at
random.The set A is reconstructed by replacing the elements of ( P ) and
another subset ( Q ) of ( A ) is chosen at
random. The probability that ( boldsymbol{P} cap boldsymbol{Q} )
contains exactly ( m(m<n) ) elements is
( ^{A} cdot frac{3^{n cdot m} cdot m^{n}}{^{n}} )
В. ( frac{n_{C_{m}} times 3^{m}}{4^{n}} )
c. ( frac{n_{m_{m} times 3^{n . m}}}{4^{n}} )
D. None of these
12
80The chances of defective screws in three
boxes ( A, B ) and ( C ) are ( frac{1}{5}, frac{1}{6}, frac{1}{7} ) respectively. A box is selected at
random and a screw drawn from it at
random, is found to be defective.

The probability that it came from the
box’A’ is
A ( cdot frac{16}{29} )
B. ( frac{1}{15} )
c. ( frac{27}{59} )
D. ( frac{42}{107} )

12
81A card is draw from a well-shuffled pack
of 52 cards. What is the probability that a card will be a king?
12
82Suppose a girl throws a die. If she gets 1 or ( 2, ) she tosses a coin three times and notes the number of tails. If she gets
3,4,5 or ( 6, ) she tosses a coin once and
notes whether a ‘head’ or ‘tail’ is
obtained. If she obtained exactly one
tail’, what is the probability that she
threw 3,4,5 or 6 with the die?
12
83The probability that Dhoni will hit
century in every ODI matches he plays is ( frac{1}{5} ). If he plays 6 matches in World Cup ( 2011, ) the probability that he will score 2 centuries is:
A ( cdot frac{768}{3125} )
в. ( frac{2357}{3125} )
c. ( frac{2178}{3125} )
D. ( frac{412}{3125} )
12
84A coin is tossed 5 times. The probability of 2 heads and 3 tails is:
A ( cdot frac{11}{16} )
B. ( frac{5}{16} )
c. ( frac{11}{32} )
D. ( frac{5}{32} )
12
85A box contains 20 identical balls of
which 5 are white and 15 black. The
balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn fro
the ( 3^{r d} ) time on ( 6^{t h} ) drawn is
12
86If ( A ) is any event in a sample space, then ( boldsymbol{P}(overline{boldsymbol{A}})=mathbf{1}+boldsymbol{P}(boldsymbol{A}) )
A. True
B. False
c. Either
D. Neither
12
87Fifteen coupons are numbered ( 1,2, ldots . .15 )
respectively. Three coupons are selected at random without replacement. The probability that the maximum number on the selected coupon is ( 9, ) is
A ( cdot 4 / 65 )
в. ( 3 / 65 )
( mathrm{c} cdot 1 / 13 )
D. None of these
12
88A box contain card number 11 to ( 123 . ) A
card is drawn at random from the find
the probability that the number on the drawn card is
(ii) a multiple of 7
12
89For any two events ( A ) and ( B ) in a sample
space
This question has multiple correct options
( ^{mathbf{A}} cdot p(A / B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true
B ( cdot P(A cap B)=P(A)-P(bar{A} cap bar{B}) ) does not hold.
( mathbf{c} cdot P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( A ) and ( B ) are independent
D ( cdot P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint.
12
90From a deck of 52 cards, four cards are
drawn simultaneously, find the chance that they will be the four honours of the
same suit.
12
91State which of the following variables are continuous and which are discrete:
a)number of children in your class
b) distance traveled by a car
c) sizes of shoes
d) time
e) number of patients in a hospital
12
92Which of the following experiments have equally likely
outcomes?
(a) A driver attempts to start a car. The car starts or does
not start.
(b) A player attempts to shoot a basketball. She/he shoots
or misses the shot.
(c) A trial is made to answer a true-false question. The
answer is right or wrong.
(d) A baby is born. It is a boy or a girl.
12
93If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} )
then find ( boldsymbol{P}(boldsymbol{A} cap overline{boldsymbol{B}}) )
12
94If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{B})=frac{1}{5} )
then
This question has multiple correct options
A ( cdot P(A cup B)=frac{3}{5} )
в. ( P(A / B)=frac{1}{2} )
c. ( P(A / A cup B)=frac{5}{6} )
D cdot ( Pleft(A cap B / A^{prime} cup B^{prime}right)=0 )
12
95A random variable ( boldsymbol{X} ) has the following probability distribution:
Determine
(i) ( k )
(ii) ( boldsymbol{P}(boldsymbol{X}boldsymbol{6}) )
(iv) ( boldsymbol{P}(mathbf{0}<boldsymbol{X}<mathbf{3}) )
begin{tabular}{|c|c|c|c|c|c|c|c|c|}
hline ( mathrm{X} ) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
hline ( mathrm{P}(mathrm{X}) ) & 0 & ( k ) & ( 2 k ) & ( 2 k ) & ( 3 k ) & ( k^{2} ) & ( 2 k^{2} ) & ( 7 k^{2}+k ) \
hline
end{tabular}
12
96If ( boldsymbol{E} ) and ( boldsymbol{F} ) are events such that ( boldsymbol{P}(boldsymbol{E})= ) ( frac{1}{4}, P(F)=frac{1}{2} ) and ( P(E a n d F)=frac{1}{8} ) find
(i) ( P(E text { or } F) )
(ii) ( P(text { not } E text { and } operatorname{not} F) )
12
97Three numbers are chosen at random
without replacement from ( 1,2, ldots .10 . ) The probability that the minimum of the
chosen numbers is 3 , or their maximum
is ( 7, ) is
A ( cdot frac{7}{40} )
B. ( frac{5}{40} )
c. ( frac{11}{40} )
D. None of these
12
98A box contains 100 tickets numbered
( 1,2, dots .100 . ) Two tickets are chosen at
random. It is given that the minimum number on the two chosen tickets is not
more than ( 10 . ) The maximum number on
them is 5 with probability.
A.
в.
c. ( frac{1}{90} )
D.
12
99In a test an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he make, a guess is ( frac{1}{3} ) and the probability that he copies the answer is ( frac{1}{6} . ) The probability that his answer is correct given that he copied it is ( frac{1}{8} . ) Find the probability that he knew the answer to the question,
given that he correctly answered it.
12
100If two events ( A ) and ( B ) are such that
( boldsymbol{P}(boldsymbol{A})=cdot boldsymbol{2}, boldsymbol{P}(boldsymbol{B})=cdot boldsymbol{3} ) and ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
( cdot 4 ) then ( P(A cap B) ) equals?
A . 0.2
B. 0.1
( c cdot 0.3 )
D. None of these
12
101What are the possible number of outcomes if a card is drawn from a pack
of 52 cards?
A . 20
B . 30
( c cdot 42 )
D. 52
12
102Find the probability distribution of the number of doublets in three throws of a
pair of dice
12
103A bag contain 4 white and 2 black balls.
Two balls are drawn at random. The
probability that they are of the same colour is
A ( cdot frac{5}{7} )
B.
c. ( frac{7}{15} )
D. ( frac{1}{15} )
12
104If ( A ) and ( B ) are two events such that
( mathbf{2} boldsymbol{P}(boldsymbol{A})=mathbf{3} boldsymbol{P}(boldsymbol{B}), ) where ( mathbf{0}<boldsymbol{P}(boldsymbol{A})< )
( P(B)<1, ) then which one of the
following is correct?
A. ( P(A mid B)<P(B mid A)<P(A cap B) )
в. ( P(A cap B)<P(B mid A)<P(A mid B) )
c. ( P(B mid A)<P(A mid B)<P(A cap B) )
( D(A cap B)<P(A mid B)<P(B mid A) )
12
105Two dice are thrown. The number of
sample points in the sample space when six does not appear on any one side is
A . 11
B . 30
c. 18
D. 25
12
106In 50 tosses of coin tail appears 32
times. If a coin is tossed random, what
is the probability of getting head?
12
10720 card are numbered from 1 to ( 20 . ) One
card is drawn at random. What is the
probability that the number on the card is greater than ( 12 ? )
A ( cdot frac{2}{3} )
B. ( frac{1}{2} )
( c cdot frac{2}{5} )
D. None of these
12
10811.
The probability of drawing an ace from a deck of cards is
15
(a) à
(d) 52
T
..
.
hat in the chance that tomorrow will be
11
109Find the variance of numbers obtained
on thrown an unbiased die.
12
110A man is known to speak the truth 3 out of 4 times. He throws a die and reports
that it is a six. The probability that it is
actually a six is
A ( cdot frac{3}{8} )
в. ( frac{1}{8} )
( c cdot frac{1}{4} )
D.
12
111( X ) has three children in his family. The
probability of one girl and two boys is……
A ( cdot frac{1}{8} )
B. ( frac{1}{2} )
( c cdot frac{1}{4} )
D. ( frac{3}{8} )
12
112A computer producing factory has only two plants ( T_{1} ) and ( T_{2} ). Plant ( T_{1} ) produces
( 20 % ) and plant ( T_{2} ) produces ( 80 % ) of total
computers produced. ( 7 % ) of computers produced in the factory turn out to be defective. It is known that ( P ) (computer
turns out to be defective given that it is
produced in plant ( T_{1} ) ) ( =10 P ) (computer
turns out to be defective given that it is
produced in plant ( T_{2} ) ). where ( P(E) ) denotes the probability of
an event ( E . ) A computer produced in the factory is randomly selected and it does not turn out ot be defective. Then the
probability that it is produced in plant
( T_{2} ) is
A ( cdot frac{36}{73} )
в. ( frac{47}{79} )
c. ( frac{78}{93} )
D. ( frac{75}{83} )
12
113From a lot of 6 items containing 2
defective items, a sample of 4 items are
drawn at random. Let the random
variable X denote the number of
defective items in the sample. If the sample is drawn without replacement, find the probability distribution of ( X )
12
114If ( frac{1+4 p}{4}, frac{1-p}{2}, frac{1-2 p}{2} ) are
probabilities of three mutually exclusive events, then
A ( cdot frac{1}{3} leq p leq frac{1}{2} )
в. ( frac{1}{3} leq p leq frac{2}{3} )
c. ( frac{1}{6} leq p leq frac{1}{2} )
D. None of these
12
115two players ( A ) and ( B ) play a series of games of chess. The winning players in any games gets 1 points while the losing plays get 0 points. The player who achievers 4 point first, wins the series. If no game ends in draw, find the Number
of ways in which the series is can be won
by ( A )
12
116( A ) is a set containing ( n ) elements. Two subsets ( P ) and ( Q ) of ( A ) are chosen at
random. (P and Q may have elements in
common). The probability that ( boldsymbol{P} cup boldsymbol{Q} neq )
( A ) is
A ( cdot(3 / 4)^{n} )
B. 1/4n
c. ( ^{n} C_{2} / 2^{n} )
D. ( 1-(3 / 4)^{n} )
12
117( A ) and ( B ) are two events such that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{mathbf{3}}{mathbf{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= )
( frac{1}{4}, P(bar{A})=frac{2}{3} ; operatorname{then} P(bar{A} cap B) ) is
A ( .1 / 12 )
в. ( 5 / 12 )
c. ( 4 / 9 )
D. ( 1 / 3 )
12
118If for two events ( A ) and ( B, P(A cup B)= ) ( frac{1}{2}, P(A cap B)=frac{2}{5} ) and ( operatorname{then} Pleft(A^{c}right)+ )
( boldsymbol{P}left(boldsymbol{B}^{c}right) ) equals
A ( cdot frac{4}{5} )
в.
c. ( frac{11}{10} )
D. None of these
12
119An integer is chosen at random from the
first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is
A ( cdot frac{1}{4} )
B. ( frac{2}{3} )
c. ( frac{1}{5} )
( D )
12
120A fair coin is tossed 99 times. If ( X ) is the
number of times heads occur then ( P(X= )
r) is maximum when ( r ) is
( mathbf{A} cdot 49 )
B. 50
c. 51
D. none of these
12
121If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=mathbf{1} / 2 ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{5} )
then
This question has multiple correct options
A ( cdot P(A cup B)=frac{3}{5} )
B. ( P(A mid B)=frac{1}{2} )
( ^{mathbf{c}} cdot P(A mid A cup B)=frac{5}{6} )
D . ( Pleft[(A cup B) midleft(A^{prime} cup B^{prime}right)right]=0 )
12
122ff ( P(E)=0.05, ) what is the probability
of not ( ^{prime} boldsymbol{E}^{prime} ) ?
12
123A cricket team has 15 members, of
whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least
3 bowlers is
( A cdot frac{7}{13} )
B. ( frac{11}{15} )
c. ( frac{12}{13} )
D. None of these.
12
124If three events ( A, B, C ) are mutually
exclusive, then which one of the
following is correct?
A ( cdot P(A cup B cup C)=0 )
B . ( P(A cup B cup C)=1 )
c. ( P(A cap B cap C)=0 )
D cdot ( P(A cap B cap C)=1 )
12
125Only one subject
A . 0.72
B. 0.36
c. 0.48
D. 0.24
12
126If ( A ) and ( B ) are two events, then, ( 1+ )
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})-boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(boldsymbol{A}) ) is equal to
( mathbf{A} cdot P(bar{A} cup bar{B}) )
B ( cdot P(A cap bar{B}) )
( mathbf{c} cdot P(bar{A} cap B) )
D ( cdot P(A cup B) )
E ( cdot P(bar{A} cap bar{B}) )
12
127The number of ways of arraigning 6 players to throw the cricket ball so that the oldest player may not throw first is
A .120
в. 600
( c .720 )
D. 715
12
128The probability of an event ( A+ ) Probability of the event ‘not ( A^{prime}= )12
129There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random.
If ( A ) is the event that the number on the
ticket is a prime number less than 15 write the sample space ( S, n(S) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) )
12
130The probability that the value of certain stock will remain the same is ( 0.46 . ) The probability that its value will increase
by Rs. 0.50 or Re. 1 per share are respectively 0.17 and 0.23 and the probability that its value will decrease by Rs. 0.25 per share is 0.14 . The expected gain per share is
A . Rs. 0.75
B. Rs. 0.25
c. Rs. 0.28
D. Rs. 0.50
12
131Consider the following relations
( (1) boldsymbol{A}-boldsymbol{B}=boldsymbol{A}-(boldsymbol{A} cap boldsymbol{B}) )
(2) ( boldsymbol{A}=boldsymbol{A}-(boldsymbol{A} cap boldsymbol{B}) cup(boldsymbol{A}-boldsymbol{B}) )
(3) ( boldsymbol{A}-(boldsymbol{A} cup boldsymbol{C})=(boldsymbol{A}-boldsymbol{B}) cup(boldsymbol{A}-boldsymbol{C}) )
Which of these is correct
A . 1 and 3
B. 2 only
( c cdot 2 ) and 3
D. 1 and 2
12
132If ( P(A)=frac{1}{3}, P(B)=frac{1}{2} ) and ( A, B ) are
mutually exclusive, find ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right) )
A ( cdot frac{5}{6} )
B.
( c cdot frac{1}{5} )
D.
12
133While doing any experiment, there will be a possible outcome which is called
A. An impossible event
B. A sure event
c. An exhaustive event
D. A complementary event
12
134An old man while dialing a 7 digit telephone number remembers that the
first four digits consists of one ( 1^{prime} s, ) one
( 2^{prime} s ) and two ( 3^{prime} s . ) He also remembers that
the fifth digit is either a 4 or 5 while has no memorizing of the sixth digit, he remembers that the seventh digit is 9
minus the sixth digit. Maximum
number if distinct trails he has to try
make sure that he dials the correct
telephone number, is
A . 360
B . 240
c. 216
D. none
12
135For the following distribution function ( F(x) ) of a r.v ( X ) is given
[
begin{array}{ccccc}
x & 1 & 2 & 3 & 4 \
F(x) & 0.2 & 0.37 & 0.48 & 0.62
end{array}
]
Then ( P(3<x leq 5)= )
A . 0.48
в. 0.37
c. 0.27
D. 1.47
12
136A die is thrown. If ( A ) is the event that the
number on upper face is a prime, then
write sample space and event ( boldsymbol{A} ) in set
notation.
12
137( ln ) a shop ( X, 30 ) tin pure ghee and 40 tin adultered ghee are kept for sale while in
shop ( Y, 50 ) tin pure ghee and 60 tin adultered ghee are there. One tin of ghee is purchased from one of the shops randomly and it is found to be adultered. Find the probability that it is
purchased from shop B.
12
138In a meeting, ( 70 % ) of the members favour and ( 30 % ) oppose a certain proposal. A member is selected at
random and we take ( boldsymbol{X}=mathbf{0} ) if he
opposed, and ( X=1 ) if he is in favour.
Find ( boldsymbol{E}(boldsymbol{X}) ) and ( boldsymbol{V} boldsymbol{a} boldsymbol{r}(boldsymbol{X}) )
12
13914.
For the three events A, B, and C, P (exactly one of the events
A or B occurs) = P (exactly one of the two events B or C
occurs) = P(exactly one of the events C or A occurs) =p and
P (all the three events occur simultaneously) = p-, where
0<p<1/2. Then the probability of at least one of the three
events A, B and C occurring is
(1996 – 2 Marks)
(a) 3p+2p2
(b) P+3p?
| (@) P+3p?
(d) 3p+2p?
11
140The mean and standard deviation of a
random variable ( X ) are 10 and 5
respectively. Find.
( boldsymbol{E}left(left(frac{boldsymbol{x}-mathbf{1 0}}{mathbf{5}}right)^{2}right) )
12
141A manufacturer has three machine
operators ( A, B ) and ( C . ) The first operator ( A ) produces ( 1 % ) defective items,
whereas the other two operators ( B ) and
( C ) produce ( 5 % ) and ( 7 % ) defective items
respectively. ( A ) is on the job for ( 50 % ) of
the time, ( B ) is on the job for ( 30 % ) of the
time and ( C ) is on the job for ( 20 % ) of the
time. A defective item is produced, what is the probability that it was produced
by ( boldsymbol{A} ) ?
12
142There are two small boxes ( A ) and ( B ). ( ln A )
there are 9 white beads and 8 black
beads.
( ln B ) there are 7 white and 8 black
beads. We want to take a bead from a
box.
(a) What is the probability of getting a white bead from each box?
(b) ( A ) white bead and a black bead are
added to box ( B ) an then a bead is taken
from it.

What is probability of getting a white bead from it.

12
143If ( bar{E} ) and ( bar{F} ) are complementary events of E and F respectively and if ( 0< )
( boldsymbol{P}(boldsymbol{F})<1, ) then
This question has multiple correct options
A ( cdot P(E / F)+P(bar{E} / F)=1 )
B . ( P(E / F)+P(E bar{F})=1 )
c. ( P(bar{E} / F)+P(E bar{F})=1 )
D . ( P(E bar{F})+P(bar{E} bar{F})=1 )
12
144Let the p.m.f. of a random variable ( boldsymbol{X} ) be
( P(x)=frac{3-x}{10} ) for ( x=-1,0,1,2 )
otherwise
Then ( boldsymbol{E}(boldsymbol{X}) ) is
( mathbf{A} cdot mathbf{1} )
B . 2
c. 0
D. –
12
145A fair coin is tossed ( n ) times. if the
probability that head occurs 6 times is equal to the probability that head
occurs 8 times, then value of ( n ) is
A .24
B. 48
c. 14
D. 16
12
146If a letter is selected at random from the
letters of the word LOGARITHMS, then
what is the probability that it will be a consonant?
12
147When a die is thrown, list the outcomes
of an event of getting:
A number greater than 5
( mathbf{A} cdot mathbf{5} )
B. 4
( c .6 )
D. 3
12
148A man takes a step forward with probability 0.4 and backward with probability 0.6. Suppose the man takes
11 steps and ( p_{r} ) denotes the probability
that the man is ( r ) steps away from his initial position, then value of
12
149The probability of sample space is
A .
B.
( c cdot 1 )
D. None of these
12
150A lot contains 20 articles. The
probability that the lot contains exactly
2 defective articles is 0.4 and the
probability that the lot contains exactly
3 defective articles is ( 0.6 . ) Article are
drawn from the lot at random one by one
without replacement and are tested till all defective articles are found. What is
the probability that the testing procedure ends at the twelfth testing?
12
151The expectation of the number of heads in 15 tosses of a coin is ( frac{x}{2} . ) The value of
( x ) is
12
152Box-I contains 5 red and 4 white balls
while box-ll contains 4 red and 2 white
balls. A fair die is thrown. If it turns up a
multiple of ( 3, ) a ball is drawn, from boxelse a ball is drawn from box-II. The probability that the ball drawn is white is ( frac{a}{27} . ) Find ( a )
12
153Suppose a girl throws a die. If she gets a
5 or ( 6, ) she tosses a coin three times and
notes the number of heads. If she gets
1,2,3 or ( 4, ) she tosses a coin once and
notes whether a head or tail is obtained.
If she obtained exactly one head, what
is the probability that she threw 1,2,3 or 4 with the die?
12
154If ( bar{E} ) and ( bar{F} ) are the complementary
events of events ( boldsymbol{E} ) and ( boldsymbol{F} ) respectively
and if ( mathbf{0}<boldsymbol{P}(boldsymbol{F})<mathbf{1}, ) then
( ^{mathbf{A}} cdot_{P}left(frac{E}{F}right)+Pleft(frac{bar{E}}{F}right)=1 )
в. ( quad Pleft(frac{E}{F}right)+Pleft(frac{E}{bar{F}}right)=1 )
( ^{mathbf{c}} cdot_{P}left(frac{bar{E}}{F}right)+Pleft(frac{E}{bar{F}}right)=1 )
( Pleft(frac{E}{bar{F}}right)+Pleft(frac{bar{E}}{bar{F}}right)=1 )
12
155If ( A ) and ( B ) are two events such that
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 7} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 2} ) then ( boldsymbol{P}(boldsymbol{B}) ) is equal to
A . 0.1
B. 0.3
( c .0 .5 )
( D )
12
156Let ( A, B, C ) be three events such that ( A ) and ( mathrm{B} ) are independent and ( boldsymbol{P}(boldsymbol{C})=mathbf{0} )
then events ( A, B, C ) are
A. independent
B. pairwise independent but not totally independent
C. ( P(A)=P(B)=P(C) )
D. none of these
12
157If a coin is tossed 3 times, then the number of outcomes will be?12
158A class has 15 students whose ages are 14,17,15,14,21,17,19,20,16,18,20,17,16
19 and 20 years. One student is selected
in such a manner that each has the
same chance of being chosen and the
age ( X ) of the selected student is
recorded. What is the probability distribution of the random variable ( boldsymbol{X} ) ?
Find mean, variance and standard
deviation of ( boldsymbol{X} )
12
159An insurance company insured 2000
scooter drivers, 4000 car drivers and
6000 truck drivers. The probability of an
accidents are 0.01,0.03 and 0.15 respectively. One of the insured person meets with an accident. What is the
probability that he is a scooter driver?
12
160( A ) and ( B ) are events with ( P(A)= )
( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3} )
Find the probability that
i) A does not occur
ii) neither A nor B occurs
12
161A game of numbers has cards marked
from ( 11,12,13, ldots, 40 . ) One card is drawn at random. Find the probability that the number drawn is divisible by 7
12
162Two players ( A ) and ( B ) are competing at a trivia quiz game involving a series of questions. On any individual question,
the probabilities that ( A ) and ( B ) give the correct answer are ( alpha ) and ( beta ) respectively,
for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if B answers the first question.
A ( cdot frac{alpha}{1-(1-alpha)(1-beta)} )
в. ( frac{(1-beta)}{1-(alpha)(beta)} )
c. ( frac{(1-beta) alpha}{1-(1-alpha)(1-beta)} )
D. none of these
12
16331.
For three events A, B and C,
P(Exactly one of A or B occurs)
= P(Exactly one of B or C occurs)
=P(Exactly one of C or A occurs) = – and
P(All the three events occur simultaneously) =
16
Then the probability that at least one of the eve
occurs, is:
[JEE M 2017)
16
11
16450 plants were planted each school out of 10 schools. After a month, the number of planets that survived are given below:Find Mean and Variance
school
[
2
]
Number of planet 35
survived
12
165The queen king,jack of diamonds are removed from a deck of 52 playing cards. One card is drawn. Find the
probability of getting a card of
(i) a diamond
(ii) a jack
12
166Two cards are drawn simultaneously from a well-shuffled deck of 52 cards.
Find the probability distribution of the number of successes, when getting a spade is considered a success.
12
167Coloured balls are distributed in 3
bags.
( boldsymbol{B}_{1} rightarrow mathbf{1} boldsymbol{B}, mathbf{2} boldsymbol{W}, mathbf{3} boldsymbol{R} )
( B_{2} rightarrow 2 B, 4 W, 1 R )
( boldsymbol{B}_{3} rightarrow mathbf{4} boldsymbol{B}, mathbf{5} boldsymbol{W}, mathbf{5} boldsymbol{R} )
A bag is selected at random and then 2
balls are drawn from the selected bag. They happen to be black and red. What is the probability that the balls come
from bag 1?
12
168If ( boldsymbol{P}(boldsymbol{A})=boldsymbol{P}(boldsymbol{B}), ) then the two events ( boldsymbol{A} )
and ( B ) are –
A. Independent
B. Dependent
c. Equally likely
D. Both (A) and (C)
12
169If ( P(E)=0.05, ) what is the probability of
“not E” ?
12
170Roll a die ten times and record the
outcomes in the form of table.
12
171( A ) and ( B ) are two independent events such that ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right)=frac{1}{6} ) and
( Pleft(A^{prime}right)=frac{5}{24} . ) Then ( P(B) ) is equal to
( A cdot frac{4}{5} )
B.
( c cdot frac{1}{5} )
D.
12
172The mean and the variance of a binomial distribution are 4
and 2 respectively. Then the probability of 2 successes is
[2004]
219
128
37
256
256
256
12
173A die is thrown twice. Each time the
number appearing on it is recorded. Describe the following events:
( A= ) Both numbers are odd
( B= ) Both numbers are even
( C= ) Sum of the numbers is less than 6
Also, Find ( boldsymbol{A} cup boldsymbol{B}, boldsymbol{A} cap boldsymbol{B}, boldsymbol{A} cup boldsymbol{C}, boldsymbol{A} cap boldsymbol{C} )
Which pairs of events are mutually exclusive
12
17423. IF C and
23. – If C and D are two events such that
then the correct statement among the follo
(a) P(CD) 2 PC) b) P(CD)<P(C)
ents such that C C D and P(D) 0,
among the following is [2011]
(c) P(CD)=
(d) P(CD)=P(C)
P(C)
12
175A ball is drawn at random from a box
containing 10 red, 30 white, 20 blue and
15 orange marbles. The probability of a ball drawn is red, white or blue ( ldots )
A ( cdot frac{1}{3} )
B. ( frac{3}{5} )
( c cdot frac{2}{3} )
D. ( frac{4}{5} )
12
176Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 2 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 8} )
12
177If ( P(E)=0 ) Then ( P(text { not } E) ) is
A . 1
B. – –
( c cdot 0 )
D. ( 1 / 2 )
12
178A box contains 100 tickets numbered
( 1,2,3, dots, 100 . ) two tickets are chosen at random. If it is given that the maximum
number on the two chosen tickets is not
more than 10 , then the probability that the minimum number on them is not
less than 5 is
A ( cdot frac{1}{3} )
B. ( frac{1}{5} )
c. ( frac{152}{165} )
D. None of these
12
179The probability that atleast one of the
events ( A, B ) happens is ( 0.6 . ) If probability of their simultaneously happening is ( 0.5, ) then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= )
A . 0.4
B. 0.8
c. 0.9
D. 1.
12
18013.
A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball
drawn is
(i) red (ü) not black.
11
181Suppose that the reliability of a HIV test is specified as follows:Of people having HIV, ( 90 % ) of the test detect the disease
but ( 10 % ) go undetected. Of people free of ( mathrm{HIV}, 99 % ) of the test are judged HIV-ive but ( 1 % ) are diagnosed as showing HIV+ive. From a large population of which only ( 0.1 % ) have ( mathrm{HIV} ), one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the
person actually has HIV?
12
182ales
порошо ер
11. What is the probability of choosing a vowel from the
alphabets?
T oboplonlu out of 5 students can partioint
1
11
183If the difference between the mean and
variance of a binomial distribution for 5 trials is ( frac{5}{9}, ) then the distribution is
( ^{A} cdotleft(frac{1}{9}+frac{2}{9}right)^{5} )
( ^{mathrm{B}}left(frac{1}{4}+frac{3}{4}right)^{5} )
( ^{c}left(frac{2}{3}+frac{1}{3}right)^{5} )
( ^{mathrm{D}}left(frac{3}{4}+frac{1}{4}right)^{5} )
12
184If ( P(A)=frac{3}{5} ) and ( P(B)=frac{1}{5}, ) find
( mathbf{1 0 0} boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) if ( boldsymbol{A} ) and ( boldsymbol{B} ) are
independent events.
12
185There are 2 red and 2 yellow flowers in a
basket. A child picks up at random three flowers. What is the probability of picking up both the yellow flowers?
12
186In a school, there are 20 teachers who
teach mathematics or physics. Of these,
12 teach mathematics and 4 teach both
physics and Mathematics. How many teach physics?
12
187( A ) and ( B ) two events such that ( P(A cap )
( left.boldsymbol{B}^{prime}right)=mathbf{0 . 2 0}, boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}right)=mathbf{0 . 1 5}, ) and
( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right)=mathbf{0 . 1 0}, ) then ( boldsymbol{p}(boldsymbol{A} / boldsymbol{B}) ) is
This question has multiple correct options
( ^{mathbf{A}} cdot P(A mid B)=frac{2}{5} )
в. ( P(A)=0.3 )
c. ( P(A cup B)=0.45 )
D. ( P(B mid A)=frac{1}{3} )
12
188In throwing of a die, let ( A ) be the event
‘an odd humber turns up’, ( B ) be the
event ‘a number divisible by 3 turns up’ and ( C ) be the event ‘a number ( leq 4 ) turns
up’, Then find the probability that exactly two of ( A, B ) and ( C ) occur.
A ( cdot frac{2}{3} )
B. ( frac{1}{6} )
( c cdot frac{1}{3} )
D.
12
189A signal which can be green or red with probability ( frac{4}{5} ) and ( frac{1}{5}, ) respectively, is received at station ( A ) and then
transmitted to station B. The probability of each station receiving the signal correctly is ( frac{3}{4} . ) If the signal received at station B is green, then the probability that the original signal was green is
( A cdot frac{3}{5} )
B. ( frac{6}{7} )
c. ( frac{20}{23} )
D. ( frac{9}{20} )
12
190Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the Probability that both are king.12
191A letter is chosen at random from the
letters of the English alphabet The
probability that it is not a vowel is
A . 5/26
B. 21/26
c. ( 15 / 26 )
D. ( 1 / 2 )
12
192One hundred identical coins, each with
probability, ( p, ) of showing up heads are
tossed once. If ( 0<p<1 ) and the
probability of heads showing on fifty coins is equal to that of heads showing on 51 coins, then the value of ( p ) is :
A . ( 1 / 2 )
B . ( 49 / 101 )
c. ( 50 / 101 )
D. ( 51 / 101 )
12
193State true or false
A probability experiment was conducted. Following number is considered as a probability of an outcome?
( mathbf{1 . 4 5} )
A. True
B. False
12
194Cards marked with numbers 4 to 99 are
placed in a box and mixed thoughtly. One card is drawn from this box. Find
the probability that the number on the card is a prime number less than 30
12
195If ( P(n) ) is the statement ( ^{prime prime} n^{2} ) is even”
then what is ( boldsymbol{P}(mathbf{9}) ) ?
12
196A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, then the probability that either both are apples or both are ( operatorname{good} ) is ( frac{316}{435} )
A. True
B. False
12
197A bag contains 8 black and 5 white
balls. 2 balls are drawn. Find the
probability that both the balls are white.
12
198Tne probability that Krishna will be alive
10 years is ( frac{7}{15} ) and that Hari will be alive
is ( frac{7}{10} . ) The probability that both Krishna
and Hari will be dead is –
A ( cdot frac{21}{150} )
B. ( frac{24}{150} )
( mathbf{c} cdot frac{49}{150} )
D. ( frac{56}{150} )
12
199(d) 1
A student appears for tes
successful if he passes eit
III. The probabilities o
pears for tests I, II and III. The student is
fiul if he passes either in tests I and II or tests I and
habilities of the student passing in tests I, II and
I are p, q and
respectively. If the probability that the
student is successful is -, then
(1986 – 2 Marks)
(a) p=q=1
(b) p=9=
(d) p=
(©) p=1,q=0
(e) none of these
12
200IfE and Fare independent events such that 0<P(E) <1 and
0<P(F)< 1, then
(1989 – 2 Marks)
(a) E and Fare mutually exclusive
(6) E and FC (the complement of the event F) are
independent
© E and FC are independent
) P(E|F) + P(E|F)=1.
1 Dinle
12
201A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who
applied. Each Year-III’s name is placed in the lottery 3 times; each Year-II’s name, 2 times and Year-l’s name, 1 time.
What is the probability that a Year-III’s name will be chosen?
( A cdot )
B.
( c cdot frac{3}{3} )
( D )
12
202Let ( boldsymbol{E} ) and ( boldsymbol{F} ) be two independent events.
The probability that both ( boldsymbol{E} ) and ( boldsymbol{F} )
happens is ( 1 / 6 ) and the probability that neither ( boldsymbol{E} ) nor ( boldsymbol{F} ) happens is ( mathbf{1} / mathbf{3} ). Then This question has multiple correct options
A ( cdot P(E)=1 / 2, P(F)=1 / 3 )
B . ( P(E)=1 / 2, P(F)=1 / 6 )
C ( cdot P(E)=1 / 6, P(F)=1 / 2 )
D cdot ( P(E)=1 / 3, P(F)=1 / 2 )
12
20325. Four fair dice D2,D , Dą and Di; each having six faces
numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously.
The probability that DA shows a number appearing on one
of D1, D2 and D3 is
(2012
91
216
(a)
108
(b) 216
125
(©) 216
127
(d) 216
1
1
.1
11
204( A ) and ( B ) are two events on a sample
space ( S ) such that ( P(A)=0.8, P(B)= )
( mathbf{0 . 6} ) and ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 9} ) find ( (boldsymbol{A} cap boldsymbol{B}) )
A . 0.3
B. 0.4
( c cdot 0.5 )
D. 0.6
12
205In a simultaneous throw of a pair of dice, find the probability of getting a
total more than 7 .
12
206If ( A ) and ( B ) are two events such that
( boldsymbol{P}(boldsymbol{A})=mathbf{1} / 2 ) and ( boldsymbol{P}(boldsymbol{B})=2 / 3, ) then
This question has multiple correct options
A. ( P(A cup B) geq 2 / 3 )
B . ( Pleft(A cap B^{prime}right) leq 2 / 3 )
c. ( 1 / 6 leq P(A cap B) leq 1 / 2 )
D. ( 1 / 6 leq Pleft(A^{prime} cap Bright) leq 1 / 2 )
12
207An unbiased coin is tossed. If the result
is a head, a pair of unbiased dice is rolled and the number obtained by
adding the numbers on the two faces is noted. If the result is a tail, a card from
a well shuffled pack of eleven cards numbered ( 2,3,4, dots . .12 ) is picked and the number on the card is noted. The
probability that the noted number is
either 7 and 8 is ( 1 k 3 / 792 ),where ( k ) is
ten’s place of the number ( 1 k 3 . ) F ind the
value of ( k .{1 k 3=100+10 times k+3} )
12
208( 10 % ) of the tools produced by a machine are defective. Find the probability distribution of the number of defective
tools when 3 tools are drawn one by one with replacement.
12
209In a binomial distribution ( Bleft(n, p=frac{1}{4}right) ) if the probability of at least one success is greater than or equal to ( frac{9}{10}, ) then ( n ) is greater than
A ( cdot frac{1}{log _{10} 4+log _{10} 3} )
В. ( frac{9}{log _{10} 4-log _{10} 3} )
c. ( frac{4}{log _{10} 4-log _{10} 3} )
D. ( frac{1}{log _{10} 4-log _{10} 3} )
12
210For a random experiment, all possible outcomes are called
A. numerical space.
B. event space
c. sample space.
D. both b and c
12
211The probability that there would be 1,2
or 3 persons riding a bicycle are 0.85,0.12 and 0.03 respectively. The expected number of persons per bicycle is
A . 2
B.
c. 1.18
D. 3
12
212A box contains 6 green balls, 4 blue balls and 5 yellow balls. A ball is drawn at random. Find the probability of
(a) Getting a yellow ball.
(b) Not getting a green ball.
A ( cdot frac{1}{5}, frac{1}{3} )
в. ( frac{4}{15}, frac{3}{15} )
c. ( frac{1}{3}, frac{3}{5} )
D. ( frac{2}{3}, frac{1}{15} )
12
213In a multiple choice question, there are
four alternative answer of which one or
more than one is correct. A candidate
will get marks on the question only if he ticks all the correct answer. The
candidate decides to tick all the correct
answer. The candidate decides to tick
answers at random. If he is allowed up to three chances to answer the
question, the probability that he will get marks on it is
( A cdot frac{1}{2} )
B.
( c cdot frac{1}{4} )
D. 5
12
214Suppose ( n(geq 3) ) persons are sitting in row. Two of them are selected at
random. The probability that they are not together is
A ( cdot 1-frac{2}{n} )
в. ( frac{2}{n-1} )
c. ( _{1-frac{1}{n}} )
D. None of these
12
215The marks secured by 400 students in a Mathematics test were normally distributed with mean ( 65 . ) If 120
students got marks above 85 , the number of students securing marks between 45 and 65 is
A . 120
B . 20
c. 80
D. 160
12
216If ( A ) and ( B ) are two events, then which of
the following does not represent the
probability of at most one of ( A, B ) occurs.
( mathbf{A} cdot 1-P(A cap B) )
B . ( P(bar{A})-P(bar{B})+-P(bar{A}+bar{B}) )
( mathbf{c} cdot P(bar{A})+P(bar{B})+-P(bar{A} cap bar{B}) )
( mathbf{D} cdot P(A cap bar{B})+P(bar{A} cap bar{B})-P(bar{A} cap bar{B}) )
12
217A coin is tossed for 50 times and get a
head 10 times, this action is called
A. space
B. experiment
c. sample
D. event
12
218Only tenth-, eleventh-, and twelfth-
grade students attend Washington High School. The ratio of tenth graders to the
school’s total student population is 86:
( 255, ) and the ratio of eleventh graders to
the school’s total student population is
( 18: 51 . ) If a student is selected at
random from the entire school, the
grade in which the student is most likely to be is:
A. Tenth
B. Eleventh
c. Twelfth
D. All grades are equally likely
E. Cannot be determined from the given information
12
219A bag ( A ) contains 2 white and 3 red balls
and a bag ( B ) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bags and is found to be red. The probability that it was drawn from ( operatorname{bag} B ) is ( frac{25}{X}, ) then find the value of ( X )
12
220A random variable ( X ) has the following probability distribution:
[
begin{array}{lllll}
boldsymbol{X} & 0 & 1 & 2 & 3 \
P(X= & frac{1}{4} & 2 a & 3 a & 4 a
end{array}
]
Then ( P(1 leq X leq 4) ) is:
A. ( frac{10}{21} )
в.
c. ( frac{1}{14} )
D.
12
221Two dice are thrown simultaneously. If ( X ) denotes the number of sixes, find the
expectation of ( boldsymbol{X} )
12
222A parents has two children. If one of
them is boy, then the probability that other is, also a boy, is
A ( cdot frac{1}{2} )
B. ( frac{1}{4} )
( c cdot frac{1}{3} )
D. None of these
12
223The scores on standardized admissions
test are normally distributed with a mean of 500 and a standard deviation
of ( 100 . ) What is the probability that a randomly selected student will score between 400 and 600 on the test?
A. About ( 63 % )
B. About ( 65 % )
c. About ( 68 % )
D. About ( 70 % )
12
224A bag contains 4 blue, 5 red and 7 green balls. If 4 balls are drawn one by one
with replacement, what is the probability that all are blue?
A ( cdot frac{1}{16} )
в.
c. ( frac{1}{256} )
D. ( frac{1}{64} )
12
225Two coins are tossed simultaneously.
Write the sample space ( ^{prime} S^{prime} ) and the
number of sample point ( n(S) . A ) is the
event of getting no head. Write the event ( A ) in set notation and find ( n(A) )
12
226An urn contains 10 balls coloured either
black or red When selecting two balls
from the urn at random, the probability
that a ball of each color is selected is
( 8 / 15 . ) Assuming that the urn contains more black balls then red balls, the
probability that at least one black ball is selected, when selecting two balls, is
( mathbf{A} cdot frac{18}{45} )
B. ( frac{30}{45} )
c. ( frac{39}{45} )
D. ( frac{41}{45} )
12
227OOOOOOO
10.
An unbiased die with faces marked 1,2,3,4,5 and 6 is rolled
four times. Out of four face values obtained, the probability
that the minimum face value is not less than 2 and the
maximum face value is not greater than 5, is then:
(1993 – 1 Mark)
(a) 16/81 (b) 1/81 (c) 80/81 (d) 65/81
11
228In a bag there are 6 white and 4 black
balls. Two balls are drawn one after
another without replacement.ff the 1 st ball is known to be white, the probability that the 2 nd ball drawn is also white is
( A cdot frac{2}{9} )
в. ( frac{5}{9} )
( c cdot frac{8}{9} )
D. ( frac{8}{13} )
12
229In a two child family, one child is a boy. What is the probability that the other child is a girl?12
230If ( A ) and ( B ) are two events, then which of
the following does not represent the
probability that exactly one of ( A, B )
occurs is
This question has multiple correct options
( mathbf{A} cdot P(A)+P(B)-P(A cap B) )
B ( cdot Pleft(A cap B^{prime}right)+Pleft(A^{prime} cap Bright) )
( mathbf{c} cdot Pleft(A^{prime}right)+Pleft(B^{prime}right)-2 Pleft(A^{prime} cap B^{prime}right) )
D ( . P(A)+P(B)-2 P(A cap B) )
12
231Two numbers are selected at random
from the number ( 1,2, ldots, n . ) Let ( p ) denote the probability that the difference
between the first and second is not less
than ( m ) (where ( 0<m<n ) ). If ( n=25 )
and ( boldsymbol{m}=mathbf{1 0}, ) find ( mathbf{5} boldsymbol{p} )
12
232Consider the following events for a family with children
[
A={o f text { both sexes }} ; B=
]
( {a t text { most one boy }} )
In which of the following (are/is) the events ( A ) and ( B ) are independent
(a)If a family has 3 children
(b) If a
family has 2 children Assume that the birth of a boy or a girl is equally likely mutually exclusive and exhaustive
12
233An employer sends a letter to his employee but he does not receive the
reply (It is certain that employee would have replied if he did receive the letter).
It is known that one out of ( n ) letters does
not reach its destination. Find the
probability that employee does not receive the letter.
A ( cdot frac{1}{n-1} )
B. ( frac{n}{2 n-1} )
c. ( frac{n-1}{2 n-1} )
D. ( frac{n-2}{n-1} )
12
23424.
Three numbers are chosen
from {1,2,3,..8). The probability that their minimum
that their maximum is 6, is:
Pers are chosen at random without replacement
obability that their minimum is 3, given
[2012]
12
235Find the chance of throwing more than
15 in one throw with 3 dice.
12
236Three unbiased coins are tossed. What
is the probability of getting at most two tails or two heads?
( A cdot frac{3}{2} )
B. ( frac{3}{4} )
( c cdot frac{5}{2} )
D. ( frac{7}{2} )
12
237The least number of times a fair coin is
to be tossed in order that the probability of getting atleast one head is at least ( mathbf{0 . 9 9} ) is
A . 5
B. 6
( c cdot 7 )
( D )
12
238Box I contains 2 white and 3 red balls
and box II contains 4 white and 5 red
balls. One ball is drawn at random from
one of the boxes and is found to be red.
Then, the probability that it was from box ( | ), is?
( ^{mathrm{A}} cdot frac{54}{44} )
в. ( frac{54}{14} )
c. ( frac{54}{104} )
D. None of these
12
239Three balls are drawn at random from a
collection of 7 white, 12 green and 4 red balls. The probability that each is different colour is
A ( cdot frac{48}{253} )
в. ( frac{64}{253} )
c. ( frac{23}{253} )
D. ( frac{56}{253} )
12
24025.
A multinta
has three alternative answers of which
on has 5 questions. Each question
ve answers of which exactly one is correct.
dent will get 4 or more correct
[JEE M 2013]
answers just by guessing is:
10
12
241A coin is tossed repeatedly until it shows head. Let ( X ) be the number of
tosses required to get head. Write the probability distribution of ( boldsymbol{X} )
12
242Let ( omega ) be a complex cube root of unity
with ( omega neq 1 . ) A fair die is thrown three
times. If ( r_{1}, r_{2} ) and ( r_{3} ) are the numbers
obtained on the die then the probability
that ( omega^{r_{1}}+omega^{r_{2}}+omega^{r_{3}}=mathbf{0} ) is
A ( cdot frac{1}{18} )
в. ( frac{1}{9} )
( c cdot frac{2}{9} )
D. ( frac{1}{36} )
12
243State the following statement is true or
false
The probability of an event can be greater than one also.
A. True
B. False
12
244Given that she is successful, the chance
she studied for 4 hours, is
A ( cdot frac{6}{12} )
в. ( frac{7}{12} )
c. ( frac{8}{12} )
D. ( frac{9}{12} )
12
245A card is thrown from a pack of 52 cards
so that each cards equally likely to be
selected. Determine whether in the
following case are the events ( A ) and ( B ) independent. ( A= ) the card is drawn is a spade, ( B= ) the card is drawn in an ace.
12
246A letter is known to have come form
TATANAGAR or CALCUTTA. On the
envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is
A ( cdot frac{4}{11} )
в. ( frac{7}{11} )
c. ( frac{1}{22} )
D. ( frac{21}{22} )
12
247An experiment is known to be random if the results of the experiment.
A. cannot be predicted
B. Can be predicted
c. can be split into further experiments
D. can be selected at random
12
248There is ( 30 % ) chance that it rains on any particular day. Given that there is at least one rainy day in a week, what is the probability that there are at least two rainy days in the week?
A ( frac{1-4(0.7)^{7}}{1-(0.7)^{7}} )
В. ( frac{4(0.7)^{7}}{1-(0.7)^{7}} )
c. ( frac{1-(0.7)^{7}}{1-4 .(0.7)^{7}} )
D. ( frac{(0.7)^{7}}{1-4 .(0.7)^{7}} )
12
249A is known to speak truth 5 out of 7
times. What is the probability that ( boldsymbol{A} )
reports that it is a 7 when a die is
thrown?
12
250There are ( 6 % ) defective items in a large
bulk of items. Probability that a sample of 8 items will include not more than
one defective items is ( 1.42 times(0.94)^{x} )
What is the value of ( x )
12
251If the integers ( m ) and ( n ) are chosen at
random from 1 to 100 , then the
probability that a number of the form
( 7^{m}+7^{n} ) is divisible by 5 is
A ( cdot frac{1}{5} )
B. ( frac{1}{7} )
( c cdot frac{1}{4} )
D. ( frac{1}{49} )
12
252A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag.
Find the probability that one ball is red and one is green?
A . ( 19 / 20 )
B. 17/20
( c cdot 8 / 10 )
D. 21/40
( E cdot 15 / 40 )
12
253The probabilites of three events ( boldsymbol{A}, boldsymbol{B} )
and ( C ) are ( P(A)=0.6, P(B)=0.4 ) and
( boldsymbol{P}(boldsymbol{C})=mathbf{0 . 5 .} ). If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
( mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})= )
0.2 and ( P(A cup B cup C) geq 0.85, ) then
A ( cdot 0.2 leq P(B cap C) leq 0.35 )
B . ( 0.5 leq P(B cap C) leq 0.85 )
c. ( 0.1 leq P(B cap C) leq 0.35 )
D. None of these
12
254Let ( A ) and ( B ) be two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{mathbf{7}}{mathbf{1 0}} )
Then ( P(bar{B}) ) is equal to
A ( cdot frac{3}{8} )
B. ( frac{2}{7} )
( c cdot frac{7}{9} )
D. none of these
12
255For two events ( A ) and ( B ) with ( P(B) neq 1 )
prove that ( boldsymbol{P}left(boldsymbol{A} mid boldsymbol{B}^{prime}right)= )
( frac{boldsymbol{P}(boldsymbol{A})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{1-boldsymbol{P}(boldsymbol{B})} )
12
256An electric component manufactured by ‘RASU Electronics’ is tested for its defectiveness by a sophisticated testing device. Let ( A ) denote the event
“the device is defective” and ( B ) the
event “the testing device reveals the
component to be defective”. Suppose ( boldsymbol{P}(boldsymbol{A})=boldsymbol{alpha} ) and ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A})=boldsymbol{P}left(boldsymbol{B}^{prime} mid boldsymbol{A}^{prime}right)= )
( mathbf{1}-boldsymbol{alpha}, ) where ( mathbf{0}<boldsymbol{alpha}<mathbf{1}, ) then
This question has multiple correct options
( mathbf{A} cdot P(B)=2 alpha(1-alpha) )
B . ( Pleft(A mid B^{prime}right)=1 / 2 )
C ( cdot Pleft(B^{prime}right)=(1-alpha)^{2} )
D ( cdot Pleft(A^{prime} mid B^{prime}right)=[alpha /(1-alpha)]^{2} )
12
257UMU U UUvVpliv UVAUVA
13.
A fair coin is tossed repeatedly. If the tail appears on first
four tosses, then the probability of the head appearing on
the fifth toss equals
(1998 – 2 Marks)
(a) 1/2 (b) 1/32 (0) 31/32 (d) 175
12
258Rajdhani Express stops at six intermediate stations between Kota
and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is
( ^{A} cdot frac{^{6} P_{5}}{6^{5}} )
в. ( frac{^{6} C_{5}}{6^{5}} )
c. ( frac{7}{7^{5}} )
D. ( frac{7}{7^{5}} )
12
259Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is an even prime
number less than 16 .
A ( cdot frac{5}{28} )
B. ( frac{3}{50} )
( c cdot frac{3}{25} )
D. ( frac{1}{100} )
12
260There are 3 bags each containing 5
white balls and 2 black balls and 2 bags each containing 1 white balls and 4 black balls, a black ball having been drawn, find the chance that it came from the first group.
A ( cdot frac{28}{43} )
в. ( frac{15}{43} )
c. ( frac{15}{28} )
D. ( frac{13}{28} )
12
261A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is
defective is.
( ^{A} cdotleft(frac{1}{10}right)^{5} )
B. ( left(frac{1}{2}right)^{5} )
( ^{mathbf{c}} cdotleft(frac{9}{10}right) )
D. ( left(frac{9}{10}right)^{5} )
12
262A fair coin is tossed 99 times. Let ( X ) be
the number of times heads occurs. Then
( P(X=r) ) is maximum when ( r ) is
A . 49
B. 52
( c .51 )
D. None of these
12
263When a die is thrown, list the number of
outcomes of an event of getting
a number greater than 5
12
264Let ( mathbf{x}=mathbf{3}^{mathbf{n}} . ) The index ‘n’ is given a
positive integral value at random. The
probability that the value of ‘x’ will have
3 in the units place is
A . ( 1 / 4 )
B. ( 1 / 2 )
c. ( 1 / 3 )
D. ( 1 / 5 )
12
265The letters of the work “Questions” are arranged in a row at random.The probability that there are exactly two letters between ( Q ) and ( S ) is.
A ( cdot frac{1}{14} )
B. ( frac{5}{7} )
( c cdot frac{1}{7} )
D. ( frac{5}{28} )
12
266In a class of 75 students, 15 are above
average, 45 are average and the rest below average achievers. The probability that an above average achieving student fails is ( 0.005, ) that an average achieving student fails is 0.05
and the probability of a below average achieving student failing is ( 0.15 . ) If ( a ) student is know to have passed, what is
the probability that he is a below average achiever?
12
267A bag contains ( (2 n+1) ) coins. It is
known that ( n ) of these coins have a head
on both sides, whereas the remaining ( n+1 ) coins are fair. A coin is picked up
at random from the bag and tossed. If the probability that the toss results in a head is ( frac{31}{42}, ) then ( n ) is equal to
A . 10
B. 11
c. 12
D. 13
12
268The probabilities that three men hit a target are ( 1 / 6,1 / 4 ) and ( 1 / 3 . ) Each man
shoots once at the target. What is the probability that exactly one of them hits the target?
A ( cdot 11 / 72 )
B. 21/72
c. ( 31 / 72 )
D. 3/4
12
269How many play hockey only?12
270A die is thrown. Write the sample space.
If ( P ) is the event of getting an odd number, then write the event ( P ) using
set notation.
12
271If ( P(A)=0, ) then the event ( A )
A. Will never happen
B. Will always happen
c. May happen
D. May not happen
12
272IF ( P(A)=frac{1}{3}, P(B)=frac{1}{12} ) and ( P(A r )
( B)=frac{1}{36}, ) are the events ( A ) and ( B ) independent?
12
273If ( mathbf{A} ) and ( mathbf{B} ) are two events such that
( mathbf{P}(mathbf{A})=frac{mathbf{3}}{mathbf{4}} ) and ( mathbf{P}(mathbf{B})=frac{mathbf{5}}{8}, ) then
This question has multiple correct options
A ( cdot 1 geq P(A cup B) geq frac{3}{4} )
в. ( Pleft(A^{prime} cup Bright) leq frac{1}{4} )
c. ( frac{3}{8} leq P(mathrm{A} cap B) leq frac{5}{8} )
D. ( frac{1}{8} leq Pleft(A cap B^{prime}right) leq frac{3}{8} )
12
274Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a perfect square.
A ( cdot frac{9}{100} )
в. ( frac{5}{100} )
c. ( frac{4}{100} )
D. ( frac{7}{100} )
12
275A die is thrown. Find the probability of
getting:
2 or 4
12
276Drawing 4 queen cards from a well-
shuffled deck of 52 cards.
This activity is called an
A. measurement
B. experiment
c. event
D. sample
12
277An integer is chosen at random between
1 and ( 100 . ) Find the probability that it is divisible by 8 is ( frac{m}{25} . ) Find ( m )
12
278Two dice are thrown. The events ( A, B )
and ( C ) are as follows:
A : getting an even number on the first die
B : getting an odd number on the first die
C : getting the sum of the numbers on the dice ( leq 5 )

State true or false : (give reason for your answer)
(i) ( A ) and ( B ) are mutually exclusive
(ii) ( A ) and ( B ) are mutually exclusive and exhaustive
(iii) ( boldsymbol{A}=boldsymbol{B}^{prime} )
(iv) ( A ) and ( C ) are mutually exclusive
(v) ( A ) and ( B^{prime} ) are mutually exclusive
(vi) ( A^{prime}, B^{prime}, C ) are mutually exclusive and exhaustive

12
279If ( P(A)=frac{1}{8} ) and ( P(B)=frac{5}{8} . ) Which of the
following statements is correct?
A ( cdot P(A cup B) leq frac{3}{4} )
B ( cdot P(A cap B) leq frac{5}{8} )
( mathbf{c} cdot P(bar{A} cap B) leq frac{5}{8} )
D ( cdot P(A cap B) geq frac{5}{8} )
12
280In which experiment outcomes are not predictable?
A. sample
B. event
c. random
D. essential
12
281If in ( Q .104, ) we are told that a white ball
has been drawn, find the probability
that it was drawn from the first urn.
( ^{A} cdot frac{5}{9} )
в. ( frac{2}{3} )
c. ( frac{2}{9} )
D. ( frac{7}{9} )
12
282Entry to a certain University is determined by a national test. The scores on this test are normally
distributed with a mean of 500 and a
standard deviation of ( 100 . ) Tom wants to
be admitted to this university and he knows that he must score better than at
least ( 70 % ) of the students who took the
test. Tom takes the test and scores 585
Tom does better than what percentage
of students?
A. ( 89.23 % )
B. ( 77.26 % )
c. ( 70.23 % )
D. ( 80.23 % )
12
283From a pack of cards two are
accidentally dropped probability they are of opposite shade is
A ( cdot frac{13}{51} )
в. ( frac{1}{52 times 51} )
c. ( frac{26}{51} )
D. None of these
12
284A coin is tossed three times, where
(i) ( E: ) head on third toss, ( F: ) heads on
first two tosses
(ii) ( E: ) at least two heads, ( F: ) at most
two heads
(iii) ( E: ) at most two tails, ( F: ) at least
one tail.
12
28526.
Three boys and two girls stand in a queue. The probability,
that the number of boys ahead of every girl is at least one
more than the number of girls ahead of her, is
(JEE Adv. 2014)
11
286An urn contains five balls alike in every respect save colour. If three of these
balls are white and two are black and
we draw two balls at random from this
urn without replacing them. If A is the event that the first ball drawn is white and ( mathrm{B} ) the event that the second ball
drawn is black, are ( A ) and ( B )
independent? If ( A ) and ( B ) are independent then enter 1 , else enter 0 .
12
287Only one subject
A ( cdot frac{14}{25} )
в. ( frac{11}{25} )
c. ( frac{13}{25} )
D. ( frac{12}{25} )
12
288In a class there are 14 boys and 10 girls If
one child
is absent the probability that it is a boy is
A ( cdot frac{5}{12} )
в. ( frac{7}{12} )
c. ( frac{10}{14} )
D.
12
289If Republic Day falls on Friday this year and Shyam was born on 4 days before 12th January, then he celebrates his birthday on
A. Tuesday
B. Sunday
c. Monday
D. wednesday
12
290An experiment can result in only 3 mutually exclusive events ( A, B ) and ( C )
If ( boldsymbol{P}(boldsymbol{A})=mathbf{2} boldsymbol{P}(boldsymbol{B})=mathbf{3} boldsymbol{P}(boldsymbol{C}), ) then
( boldsymbol{P}(boldsymbol{A})= )
( A cdot frac{6}{11} )
B. ( frac{5}{11} )
( c cdot frac{9}{11} )
D. None
12
291Two small square on a chess board are
chosen at random. Probability that they have a common side is
A ( cdot frac{1}{3} )
в. ( frac{1}{9} )
c. ( frac{1}{18} )
D. None of these
12
292State and prove Baye’s theorem.12
293In a bolt factory, three machines ( A, B )
and ( C ) manufacture ( 25 %, 35 % ) and ( 40 % )
of the total production respectively. Of
their respective outputs, ( 5 %, 4 % ) and ( 2 % ) are defective. A bolt is drawn at random
from the total production and it is found to be defective. Find the probability that
it was manufactured by machine ( C )
12
294Find the binomial distribution for which
the mean is 4 and variance 3
12
29528.
Let two fair six-faced dice A and B be thro
If E, is the event that die A shows up
that die B shows up two and Ez is the
numbers on both dice is odd, then w
statements is NOT true?
(a) E, and E, are independent.
(b) E,, E, and E, are independent.
(c) E, and E, are independent.
(d) E, and E, are independent.
iced dice A and B be thrown simultaneously.
vent that die A shows up four, E, is the event
ws up two and E, is the event that the sum of
th dice is odd, then which of the following
[JEEM 2016
12
296A and B are mutually exclusive events,
then
( mathbf{A} cdot P(A) leq P(bar{B}) )
B ( . P(mathrm{A})>P(bar{B}) )
( mathbf{c} cdot mathrm{P}(mathrm{A})<mathrm{P}(mathrm{B}) )
D. ( P(A)=P(B) )
12
297An article manufactured by a company
consists of two parts ( X ) and ( Y . ) In the
process of manufacture of the part ( boldsymbol{X} . mathbf{9} )
out of 100 parts may be defective.
Similarly 5 out of 100 are likely to be
defective in part ( Y ). Calculate the
probability that the assembled product will not be defective.
12
298When a coin is tossed in an experiment, the result is either a head or a tail. A
head is given a point value of 1 and ( a ) tail is given a point value of ( -1 . ) If the sum of the point values after 50 tosses
is ( 14, ) how many of the tosses must
have resulted in heads?
A . 14
B. 18
c. 32
D. 36
E. 39
12
299Two numbers ( X ) and ( Y ) are chosen at
random (without replacement) from the ( operatorname{set} 1,2, dots, 5 N . ) The probability that
( X^{n} sim Y^{n} ) is divisible by 5 is
A ( frac{N-1}{5 N-1} )
в. ( frac{4(4 N-1)}{5(5 N-1)} )
c. ( frac{17 N-5}{5(5 N-1)} )
D. None of these
12
300( A, B, C ) are pair wise independent.
A. True
B. False
12
301A class consists of 100 students, 25 of
them are girls and 75 boys, 20 of them are rich and remaining poor, 40 of them are fair complexioned. The Probability of selecting a fair complexioned rich girl is
12
302Out of 50 tickets numbered
( 00,01,02, ldots ., 49 ) one ticket is drawn randomly, the probability of the ticket
having the product of its digits 7 given that the sum of the digits is ( 8, ) is
A ( cdot frac{1}{14} )
B. ( frac{3}{14} )
( c cdot frac{1}{5} )
D. None of these
12
30316
5.
Events A, B, C are mutually excl
e mutually exclusive events such that
P(A) = 3x+1, P(B) = 1-* and PCC) – 1-2x The set of
possible values of x are in the interval.
[2003]
(a) [0,1] (b)
(a) 53)
11
304A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of
10. If we can approximate the distribution of these grades by a normal distribution, what percent of the
students should fail the test (grades ( < )
60)( ? )
A . 15.21
в. 23.2
c. ( 15.87 % )
D. 16.23
12
305There are four kinds of trees in an
orchard. Four part of total trees are Neem trees. Half of the remaining trees
are Mango trees. Half of the remaining trees are Drumstick trees and the
remaining 6 trees are Peepel trees. Find the total number of trees in the orchard.
12
306Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the
drawn card is more than 3 , what is the
probability that it is an even number?
12
307Three coins are tossed. Describe
three events ( A, B ) and ( C ) which are
mutually exclusive and exhaustive
12
308There are 45 boys and girls in a class. Given the probability that a boy is chosen is ( frac{4}{15} . ) Find the number of girls
( A cdot 8 )
B. 12
c. 25
D. 33
12
309Assertion
If ( A, B, C ) are three events such that ( P(A)=frac{1}{4}, P(B)=frac{1}{6} & P(C)=frac{2}{3} )
then events ( A, B, C ) are mutually exclusive.
Reason
If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})+ )
( boldsymbol{P}(boldsymbol{C}) ) then ( A, B, C ) are mutually
exclusive events.
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
310Three coins are tossed once. Let ( boldsymbol{A} )
denote the event ‘three heads show”, ( boldsymbol{B} )
denote the event “two heads and one tail
show” ( C ) denote the event “three tails
show” and ( D ) denote the event ‘a head
shows on the first coin” Which events
are
(i) mutually exclusive?
(ii) simple?
(iii) compound?
12
311From a pack of 52 playing cards, face
cards and tens are removed and kept aside then a card is drawn at random
from the remaining cards. If
A : The event that the card drawn is an
ace
( mathrm{H}: ) The event that the card drawn is a
heart
S : The event that the card drawn is a
spade then which of the following holds?
This question has multiple correct options
( mathbf{A} cdot 9 P(A)=4 P(H) )
B . ( P(S)=4 P(A cap H) )
c. ( 3 P(H)=3 P(A cup S) )
D. None of these
12
312A bag contains 15 white and some black
balls. If the probability of drawing a black ball from the bag is thrice that of
drawing a white ball, find the number of black balls in the bag.
12
313What is the probability that a two digit number selected at random will be a
multiple of 3 and not a multiple of ( 5 ? )
A ( cdot frac{1}{15} )
в. ( frac{3}{15} )
c. ( frac{4}{15} )
D. ( frac{5}{15} )
12
314At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidate who
are really capable, ( 80 % ) pass the test and of the incapable, ( 25 % ) pass the test. Given that ( 40 % ) of the candidates are
really capable, then the proportion of capable college students is about
A . ( 68 % )
B. 70%
c. ( 73 % )
D. 75%
12
315The mathematical study of randomness is called probability theory.
A. True
B. False
c. Partly true
D. None of above
12
316The variance of the random variable ( x )
whose probability distribution is given
by
( boldsymbol{X}=boldsymbol{x}: quad mathbf{0} quad mathbf{1} quad mathbf{2} quad mathbf{3} )
( boldsymbol{p}(boldsymbol{X}=boldsymbol{x}): quad frac{1}{3} frac{1}{2} boldsymbol{0} frac{1}{boldsymbol{6}} )
A . 0.5
B. 1
( c .1 .5 )
D. 2.0
12
317An article manufactured by a company
consists of two parts ( X ) and ( Y . ) In the
process of manufacture of the part ( boldsymbol{X} . mathbf{9} )
out of 100 parts may be defective.
Similarly 5 out of 100 are likely to be
defective in part ( Y ). Calculate the
probability that the assembled product will not be defective.
12
3185 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that there are exactly 3 hearts is
A. ( frac{13}{^{13} s_{3}+^{13} c_{4}+^{13} c_{5}} )
в.
( c )
D. ( frac{13}{^{13} s_{3} times^{13} c_{4} times^{13} c_{5}} )
12
319For any two events ( A ) and ( B )
( mathbf{A} cdot P(A)+P(B)>P(A cap B) )
B ( cdot P(A)+P(B)<P(A cap B) )
( mathbf{c} cdot P(A)+P(B) geq P(A cap B) )
D ( . P(A) times P(B) leq P(A cap B) )
12
320A bag contains 25 tickets, numbered from 1 to ( 25 . ) A ticket is drawn at
random. Find the probability that the ticket will show even number.
12
321Define probability of an event?12
322The probability that a person will get an electric contract is ( frac{2}{5} ) and the probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) what is the probability that he will get both?12
32317.
A ship is fitted with three engines E , E, and Ez . The
engines function independently of each other with
1 1
respective probabilities and -. For the ship to be
2 4 4
operational at least two of its engines must function. Let
X denote the event that the ship is operational and let X,
X, and X, denote respectively the events that the engines
E, E, and E, are functioning. Which of the following
is(are) true ?
(2012)
(a) P[xx[x]=1
(b) P [Exactly two engines of the ship are functioning
(C) P[X|X2]=
(a) P[X]X1] = 16
12
324Following is the distribution function
( (x) ) of a discrete ( r . v . x )
( F(x) ) begin{tabular}{l}
0.2 \
hline
end{tabular} 0.37 ( begin{array}{ll}text { 0.48 } & text { 0.62 }end{array} )
(i) Find the probability distribution of ( x )
(ii) Find ( P(x leq 3),(2<x<5) )
12
325If ( M ) and ( N ) are any two events, the
probability that the exactly one of them
occurs is
This question has multiple correct options
A ( cdot P(M)+P(N)-2 P(M cap N) )
B . ( P(M)+P(N)-P(M cap N)^{c} )
( mathbf{c} cdot Pleft(M^{c}right)+Pleft(N^{c}right)-2 Pleft(M^{c} cap N^{c}right) )
D ( Pleft(M cap N^{c}right)+Pleft(M^{c} cap Nright) )
12
326ff ( x ) follows the Binomial distribution
with parameters ( n=6 ) and ( p ) and
( mathbf{9} P(X=4)=P(X=2), ) then ( p ) is
A ( cdot frac{1}{4} )
B.
( c cdot frac{1}{2} )
D. ( frac{2}{3} )
12
327If ( A ) and ( B ) are events such that
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) )
12
328A single 6 -sided die is rolled. What is the probability of rolling a 4 on the die?
A ( cdot frac{1}{12} )
B. ( frac{2}{3} )
( c cdot frac{3}{2} )
D.
12
329A box contains ( b ) blue balls and ( r ) red
balls. A ball is drawn randomly from the box and is returned to the box with
another ball of the same colour. The
probability that the second ball drawn from the box is blue is
A ( cdot frac{b}{r+b} )
в. ( frac{b^{2}}{(r+b)^{2}} )
c. ( frac{b+1}{r+b+1} )
D. ( frac{b(b+1)}{(r+b)(r+b+1)} )
12
330A letter is known to have come either
from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or ( boldsymbol{C A L} boldsymbol{C U T T A} )
On the envelope just two consecutive
letters ( T A ) are visible. What is the
probability that the letter came from ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{R} ? )
A ( .1 / 11 )
в. ( 7 / 9 )
c. ( 4 / 11 )
D. ( 7 / 11 )
12
331A bag contains 6 white, 5 black and 4
red balls. Find the probability of getting either a white or a black ball in a single
draw. If the answer is ( a / b, ) where HCF of
( a ) and ( b ) is ( 1, ) then find ( b-a ? )
12
332A dice is manufactured in such a way
that probability of getting an even number is twice likely to occur as an odd number. If the dice is tossed twice,
find the probability distribution of the
random variable representing the perfect square in the both tosses.
12
333The standard deviation ( sigma ) of ( (q+p)^{16} ) is
2. The mean of the distribution is
( A cdot 2 )
B. 8
c. 16
D. 20
12
334Match the follwoing12
335A purse contains 2 silver and 4 copper
coins. ( A ) second purse contains 4 silver
and 3 copper coins. If a coin is pulled at random from one of the two purses,
what is the probability that it is a silver ( operatorname{coin} )
12
336When two coins are tossed one after
another list the outcomes of getting at least one head.
( mathbf{A} cdot{H H} )
в. ( {H T, T H} )
c. ( {T T} )
D. ( {T H, H T, H H} )
12
337A bag contains some white and some black balls, all combinations of balls
being equally likely. The total number of
balls in the bag is ( 10 . ) If three balls are drawn at random without replacement and all of them are found to be black,
the probability that the bag contains 1
white and 9 black balls is
A ( cdot frac{14}{55} )
B. ( frac{12}{55} )
c. ( frac{2}{11} )
D. ( frac{8}{55} )
12
338nent from a
Two cards are drawn successively with replacement from
well-shuffled deck of 52 cards. Let X denote the rande
variable of number of aces obtained in the two drawn card
Then P(X=1)+P(X=2) equals:
JEEM 2019-9 Jan (MI
(a) 49/169
(b) 52/169
(c) 24/169
(d) 25/169
12
339Suppose a girl throws a die. If she gets a
5 or ( 6, ) she tosses a coin 3 times and
notes the number of heads. If she gets
1,2,3 and 4 she tosses a coin once and
notes whether a head or tail is obtained.
If she obtained exactly one head. What
is the probability that she threw 1,2,3 or 4 with the die?
12
340Four different objects 1,2,3,4 are distributed at random in four places
marked ( 1,2,3,4 . ) What is the probability that none of the objects occupy the place corresponding to their number?
A ( cdot frac{17}{24} )
в. ( frac{3}{8} )
c. ( frac{1}{2} )
D.
12
341If ( A ) and ( B ) be two events such that
( boldsymbol{P}(boldsymbol{A})=mathbf{1} / mathbf{4}, boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{3} ) and ( boldsymbol{P}(boldsymbol{A} cup )
( B)=1 / 2 ) show that ( A ) and ( B ) are
independence events.
12
342Assertion
If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})>boldsymbol{P}(boldsymbol{A}) ) then. ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})> )
( boldsymbol{P}(boldsymbol{B}) )
Reason
fevents ( A & B ) are dependent, then ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{B})} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
343Find the probability distribution of the
number of successes in two tosses of a
die, where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die
12
344Identify and write the like terms in each
of the following groups.
(i) ( a^{2}, b^{2},-2 a^{2}, c^{2}, 4 a )
A ( cdotleft(a^{6}, 2 a^{2}right)^{2} )
В ( cdotleft(a^{2},-2 a^{2}right) )
( mathbf{C} cdotleft(a^{3}, 2 a^{2}right) )
D. ( left(a^{2}, 2 a^{3}right) )
12
345Of the students in a school, it is known
that ( 30 % ) have ( 100 % ) attendance and
70% students are irregular. Previous year results report that ( 70 % ) of all students who have ( 100 % ) attendance
attain A grade and ( 10 % ) irregular students attain A grade in their annual examination. At the end of the year, one
student is chosen at random from the
school and he was found to have an ( A )
grade. What is the probability that the student has ( 100 % ) attendance? Is regularity required only in school? Justify your answer.
12
346A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of ( 8 ? )12
347When a die is thrown, list the outcomes
of an event of getting: a prime number.
A. 2,3,5
в. 1,3,5
c. 3,5,7
D. 1,2,5
12
348If ( A & B ) are two given events, then
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) is
A. Not less than ( P(A)+P(B)-1 )
B. Not greater than ( P(A)+P(B)-P(A cup B) )
C . Equal to ( P(A)+P(B)+P(A cap B) )
D. Equal to ( P(A)+P(B)+P(A cup B) )
12
349A box contains 100 cards marked with
numbers 1 to ( 100 . ) If one card is drawn
randomly from the box. Find the probability that it bears.
(1) Even prime number.
(2) A number divisible by 7.
(3) The number at unit place is 9
12
350A card from a pack 52 cards is lost. From the remaining card of the pack, one card is drawn and is found be
heart, Find the probability that the lost cards were both hearts.
12
351The probability of a leap year having 53 Mondays is:
A ( cdot frac{2}{7} )
B. ( frac{1}{7} )
( c cdot frac{3}{7} )
D.
12
352Three men have 6 different trousers, 5
different shirts and 4 different caps.
Number of different ways in which they
can wear them is
12
353A examination consists of 8 questions in each of which one of the 5
alternatives is the correct one. On
the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternatives with equal probability, the probability that he gets more than one correct answer is equal to five alternatives with equal probability,the probability that he gets more than one correct answer is equal to
A ( cdot(0.8)^{8} )
B. ( 3(0.8)^{8} )
c. ( 1-(0.8)^{8} )
D. ( 1-3(0.8)^{8} )
12
354A coin is tossed three times. Consider
the following events:
A: No head appears
B: Exactly one head appears
C: At least two heads appear Which one of the following is correct?
A ( .(A cup B) cap(A cup C)=B cup C )
B . ( left(A cap B^{prime}right) cupleft(A cap C^{prime}right)=B^{prime} cup C^{prime} )
C ( . A cap Bleft(B^{prime} cup C^{prime}right)=A cup B cup C )
D. ( A capleft(B^{prime} cup C^{prime}right)=B^{prime} cap C^{prime} )
12
355A pair of fair dice is rolled together till a sum of 7 or 11 is obtained. Let ( p ) denote
the probability that 7 comes before 11
Find the value of ( 4 p )
12
356The author of the book “The book on
game of chance” based on probability theory is-
A. J.Cardon
B. R.S.Woodwards
c. P.S.Laplace
D. P.D.Pherma
12
357Kamal and Monika appeared for an
interview for two vacancies. The
probability of Kamal’s selection is ( frac{1}{3} ) and that of Monika’s selection is ( frac{1}{5} . ) Find the probability that both of them will be
selected.
12
358Assertion
A bag contains ( n+1 ) coins. It is known
that one of these coins has a head on
both sides while the other coins are fair.
One coins is selected at random and
tossed. If head turns up, the probability that the selected coin was fair, is ( frac{n}{n+2} )
Reason

If an event ( A ) occurs with two mutually
exclusive and exhaustive events ( boldsymbol{E}_{1} ) and
( E_{2}, ) then ( boldsymbol{P}left(frac{boldsymbol{E}_{boldsymbol{i}}}{boldsymbol{A}}right)= )
( frac{boldsymbol{P}left(boldsymbol{E}_{boldsymbol{i}}right) boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{E}_{i}}right)}{boldsymbol{P}left(boldsymbol{E}_{1}right) boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{E}_{1}}right)+boldsymbol{P}left(boldsymbol{E}_{2}right) boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{E}_{2}}right)}, boldsymbol{i}= )
( mathbf{1}, mathbf{2} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

12
359The average length of time required to
complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 30
and 50 minutes to complete the questionnaire?
A. About ( 85 % )
B. About ( 90 % )
c. About ( 95 % )
D. none
12
360A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, the probability of at least 5 successes is ( frac{49}{9^{x}} . ) Find the value of ( x )12
361If ( A ) and ( B ) are any two events such that
( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(text {Aand} B)=boldsymbol{P}(boldsymbol{A}) )
then
( mathbf{A} cdot P(B mid A)=1 )
B . ( P(A mid B)=1 )
c. ( P(B mid A)=0 )
D cdot ( P(A mid B)=0 )
12
362Let ( A ) and ( B ) be events such that
( P(A)-frac{1}{6}, P(B)=frac{1}{4} ) and ( P(A cap B)= )
( frac{1}{12} cdot operatorname{Find} P(B / A) cdot P(A / B) )
12
363If 3 coins are tossed simultaneously, the probability of 1 head and 2 tails is:
A ( cdot frac{1}{8} )
в. ( frac{3}{8} )
( c cdot frac{5}{8} )
D. ( frac{7}{8} )
12
364A bag contains 5 red balls and some
blue balls. If the probability of drawing a blue ball at random from the bag is
three times that of a red ball, find the
number of blue balls in the bag.
12
365If ( A ) and ( B ) are events such that
( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})=boldsymbol{P}(boldsymbol{B} mid boldsymbol{A}), ) then
A ( . A subset B ) but ( A neq B )
в. ( A=B )
c. ( A cap B=Phi )
D ( cdot P(A)=P(B) )
12
366If ( A ) and ( B ) are two independent events such that ( boldsymbol{P}(boldsymbol{A})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{B})=frac{mathbf{1}}{mathbf{5}} )
then
A ( cdot P(A cup B)=frac{3}{5} )
в. ( Pleft(frac{A}{B}right)=frac{1}{2} )
( ^{c} cdot pleft(frac{A}{A cup B}right)=frac{5}{6} )
( ^{mathrm{D}} cdot_{P}left(frac{A}{bar{A}} stackrel{cap}{longrightarrow} overline{bar{B}}right)=0 )
12
367Of the students in a college, it is known that ( 60 % ) reside in hostel and ( 40 % ) are
day scholars (not residing in hostel) Previous year results report that ( 30 % ) of all students who reside in hostel attain
( A ) grade and ( 20 % ) of day scholars attain
( A ) grade in their annual examination. At
the end of the year, one student is chosen at random from the college and
he has an ( A ) grade, what is the probability that the student is a hosteller?
12
368A card from pack of 52 cards is lost. From the remaining card of the pack, one card is drawn and is found to be
heart, find the probability of missing card to be
(I) heart (II) club.
12
369A bag contains ( a ) white and ( b ) black
balls. Two players, ( A ) and ( B ) alternately
draw a ball from the bag, replacing the
ball each time after the draw till on of
them draws a white ball and win the
game. ( A ) begins the game. If the
probability of ( boldsymbol{A} ) winning the game is
three times that of ( B ), the ratio ( a: b ) is
A . 1: 1
B. 1: 2
( c cdot 2: 1 )
D. None of these
12
37015.
A pair of fair dice
0.00 (a) 0.14
air of fair dice is thrown independently three times. The
hability of getting a score of exactly 9 twice is [20071
(a) 8/729 (b) 8/243 C ) 1/729 (d) 8/9
is given that the evente
12
371A bag contains 6 red balls and 8 green balls. A ball is drawn at random. What
is the probability that the ball is green
12
372In a cricket match, a batswoman hits a
boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
12
373For ( k=1,2,3 ) the box ( B_{k} ) contains ( k ) red
balls and ( (k+1) ) white balls, let
( Pleft(B_{1}right)=frac{1}{2}, Pleft(B_{2}right)=1 ) and ( Pleft(B_{3}right)= )
( frac{1}{6} cdot A ) box is selected at random and ( a ) ball is drawn from it. If a red ball is
drawn, then the probability that it has
come from box ( B_{2} ) is
A ( cdot frac{35}{78} )
в. ( frac{14}{39} )
c. ( frac{10}{13} )
D. ( frac{12}{13} )
12
37419. Four persons independently solve a certain problem corre
with probabilities
. Then the probability that the
problem is solved correctly by at least one of them is
(JEE Adv. 2013)
235
253
256
256
256
12
375The probability that a student entering a university will graduate is ( 0.4 . ) If the probability that out of 3 students of the university, only one will graduate is ( frac{432}{10^{x}} )
then the value of ( x ) is
12
376Two independent events are always mutually exclusive, If this is true enter
1, else enter 0
A. True
B. False
12
377More than 4 on atleast one of the three successive throws, If the answer is ( frac{a}{b} )
where the HCF of ( a ) and ( b ) is 1 , then find
( boldsymbol{b}-boldsymbol{a} )
12
378A coin is tossed 100 times with the
following frequencies: Head : 20. Find the probability for event having heads only.
A . 0.2
B. 0.5
c. 0.65
D. 1.5
12
379The mean and the variance of a
binomial distribution are 4 and 2
respectively. Then the probability of 2
successes is
A ( cdot frac{128}{256} )
в. ( frac{219}{256} )
c. ( frac{37}{256} )
D. ( frac{28}{256} )
12
380Rahim takes out all the hearts from the
cards. What is the probability of Picking out a diamonds.
12
381Let ( u_{1} ) and ( u_{2} ) be two urns such that ( u_{1} )
contains 3 white, 2 red balls and ( u_{2} )
contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is
drawn at random from urn ( u_{1} ) and put
into ( u_{2} . ) However, if tail appears, then 2
balls are drawn at random from ( u_{1} ) and
put into ( u_{2} . ) Now, 1 ball is drawn at
random from ( u_{2} ). Then, probability of the
drawn ball from ( u_{2} ) being white is
A ( cdot frac{13}{30} )
в. ( frac{23}{30} )
c. ( frac{19}{30} )
D. ( frac{11}{30} )
12
382In which event, the experiment is impossible?
A. Tossing a coin for head or tail
B. 5 in case of throwing a dice.
c. Rolling a dice for 7
D. Tossing a coin to get a tail.
12
383Two numbers are selected at random
(without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find ( E(X) )
A ( cdot frac{14}{3} )
B. ( frac{13}{3} )
( c cdot frac{12}{3} )
D. ( frac{11}{3} )
12
384A box contains 24 identical balls of which 12 are white
and 12 are black. The balls are drawn at random from the
box one at a time with replacement. The probability that
a white ball is drawn for the 4th time on the 7th draw is
(1984 – 2 Marks)
(a) 5/64 (b) 27/32 (c) 5/32 (d) 1/2
11 ..1:
1
1 airgeab
:+
11:1:
af
12
385The probability that a person will get an electric contract is ( frac{2}{5} ) and the probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) what is the probability that he will get both?12
386A game of chance consists of spinning
an arrow which is equally likely to come to rest pointing to one of the number
( 1,2,3, dots .12 ) as shown in Fig. What is the probability that it will point to:
(i) 10
(ii) an odd number (iii) a
number which is a multiple of 3 (iv) an
even number.
12
387A player tosses 2 fair coins. He wins Rs5
if 2 heads appear, Rs2 if head appears
and Rs1 if no head appears. Find his
expected winning amount and variance of winning amount.
12
388Three shots are fired at a target in
succession. The probabilities of a hit in the first shot is ( frac{1}{2}, ) in the second ( frac{2}{3} ) and in the third shot is ( frac{3}{4}, ) In case of exactly one hit, the probability of destroying the target is ( frac{1}{3} ) and in the case of exactly two hits ( frac{7}{11} ) an in the case of three hits is ( 1.0 . ) Find the probability of destroying the target in three shots
( A cdot 3 )
( overline{4} )
B. ( frac{3}{8} )
( c cdot frac{5}{8} )
D. 4
12
389If a coin is tossed, then the probability
that a head turns up is
A ( cdot frac{1}{2} )
B.
( c cdot frac{1}{3} )
D. ( frac{1}{6} )
12
390Let ( X ) denote the number of hours you
study during a randomly selected school day. The probability that ( X ) can
take the values of ( x, ) has the following
form, where ( k ) is some constant ( boldsymbol{P}(boldsymbol{X}=boldsymbol{x})=left{begin{array}{ll}mathbf{0}, mathbf{1} & text { if } boldsymbol{x}=mathbf{0} \ boldsymbol{K} boldsymbol{x} & text { if } boldsymbol{x}=mathbf{1} text { or } mathbf{2} \ boldsymbol{K}(mathbf{5}-boldsymbol{x}) & text { if } boldsymbol{x}=mathbf{3} text { or } mathbf{4} \ mathbf{0} & text { otherwise }end{array}right. )
What is the probability that you study.
For at least two hour.
12
391The probability of getting at least a
single ( ^{prime} 1^{prime} ) when two dice are rolled is
A ( cdot frac{11}{36} )
в. ( frac{25}{36} )
( c cdot frac{1}{6} )
D. ( frac{1}{8} )
12
392( operatorname{Let} P(A)=0.4 ) and ( P(A cup B)= )
( P(A cap B), ) find ( 5 P(B) )
12
393( A ) speaks the truth ‘3 times out of ( 4^{prime} ) and
( B ) speaks the truth ‘2 times out of 3 ‘, ( A )
die is thrown. Both assert that the
number turned up is 2. Find the probability of the truth of their assertion.
12
394( Pleft(frac{B}{A}right) ) is defined only when:
A . ( A ) is a sure event
B. ( B ) is a sure event
c. ( A ) is not an impossible event
D. ( B ) is an impossible event
12
395If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} )
then find ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) )
12
396Assume that the chances of a patient having a heart attack is ( 40 % ). It is also assumed that a meditation and yoga
course reduce the risk of heart attack by ( 30 % ) and prescription of certain drug reduces its chances by ( 25 % ). At a time a
patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?
12
397Two digit numbers are formed using the
digits 0,1,2,3,4,5 where digits are not repeated.
( P ) is the event that the number so
formed is even
( Q ) is the event that the number so
formed is greater than 50
( R ) is the event that the number so
formed is divisible by 3

Then write the sample space ( S ) and
events ( P, Q, R ) using set notation.

12
398If ( frac{1-3 p}{2}, frac{(1+4 p)}{3}, frac{1+p}{6} ) are the
probabilities of three mutually exclusive and exhaustive events,then
the set of all values of p is
B. ( left[-frac{1}{4}, frac{1}{3}right] )
c. ( left[0, frac{1}{3}right] )
( D cdot(0, infty) )
12
399A bag contains cards which are
numbered from 2 to ( 90 . ) A card is drawn
at random from the bag. Find the probability that it bears
(i) a two digit number
(ii) a number
which is a perfect square
12
400Out of 2 men and 3 women a team of
two persons is to be formed such that there is exactly one man and one woman. Write the sample space of this
experiment, then the total no. of combinations of team possible are
A . 9
B. 6
( c cdot 4 )
D. 12
12
401If ( frac{1+4 p}{4}, frac{1-p}{4}, frac{1-2 p}{4} ) are probabilities of three mutually exclusive and exclusive and exhaustive events, then the
possible value of ( p ) belong to the set
( mathbf{A} cdotleft(0, frac{2}{3}right) )
В. ( left[0, frac{1}{2}right] )
( mathbf{c} cdotleft[-frac{1}{4}, frac{1}{2}right] )
D. ( left[-frac{2}{3}, frac{2}{3}right] )
12
402It is given that event ( A & B ) are such ( operatorname{that} boldsymbol{P}(boldsymbol{A})=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{B}}right)= )
( frac{1}{2}, Pleft(frac{B}{A}right)=frac{2}{3}, ) then ( P(B)= )
( A cdot frac{1}{3} )
B. ( frac{2}{3} )
( c cdot frac{1}{2} )
D.
12
403Assertion
A fair coin is being tossed four times. Consider the following events:
A is the event all four results are the
same.

B is the event exactly one Head occurs. ( mathrm{C} ) is the event at least two Heads occur
( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})+boldsymbol{P}(boldsymbol{C})>1 )
Reason
( A, B ) and ( C ) are not Mutually Exclusive since events ( A ) and ( C ) have outcomes in
common.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

12
404There are three different Urns, Urn-I,
Urn-II and Urn-III containing 1 Blue, 2
Green, 2 Blue, 1 Green, 3 Blue, 3 Green
balls respectively. If two Urns are
randomly selected and a ball is drawn
from each Urn and if the drawn balls are
of different colours then the probability
that chosen Urn was Urn-I and Urn-II is
A ( cdot frac{1}{7} )
B. ( frac{5}{13} )
c. ( frac{5}{14} )
D. ( frac{5}{7} )
12
405Kamal and Monika appeared for an
interview for two vacancies. The
probability of Kamal’s selection is ( frac{1}{3} ) and that of Monika’s selection is ( frac{1}{5} . ) Find the probability that at least one of them will be selected.
12
406f ( A ) and ( B ) are two events associated
with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
407Find the value of ( mathrm{K} )12
408Two symmetrical dice are thrown 200 times. Getting a sum of 9 points is considered to be a success. The
probability distribution of successes is
( ^{mathbf{A}} cdotleft(200, frac{1}{9}, frac{8}{9}right) )
в. ( left(200, frac{2}{9}, frac{7}{9}right) )
( ^{mathrm{c}} cdotleft(200, frac{4}{9}, frac{5}{9}right) )
D ( cdotleft(200, frac{1}{4}, frac{3}{4}right) )
12
409If ( A ) and ( B ) are independent events such
( operatorname{that} boldsymbol{P}(boldsymbol{A})>mathbf{0}, boldsymbol{P}(boldsymbol{B})>mathbf{0}, ) then
A. ( A ) and ( B ) are mutually exclusive
B. ( A ) and ( bar{B} ) are dependent
c. ( bar{A} ) and ( B ) are dependent
( Pleft(frac{A}{B}right)+Pleft(frac{bar{A}}{B}right)=1 )
12
410A family has two children. What is the
probability that both the children are boys given that at least one of them is a boy?
12
411Thirty-two player ranked 1 to 32 are play knockout tournament. Assume that in
every match between any two players
the better ranked player wins, the
probability that ranked 1 and ranked 2 players are winner and runner up
respectively is ( p ), then the value of ( [2 / p] )
is, where [.] represents the greatest integer function.
12
412Each of the urns contains 4 white and 6
blackballs. The ( (n+1) ) th urn contains 5
white and 5black balls. One of the ( (n+1) )
urns is chosen atrandom and two balls
are drawn from it withoutreplacement and both the balls turn out to beblack.
Then the probability that the ( (n+1) ) th urn was chosen to draw the balls is ( 1 / 16 ) the value of ( n ) is
A . 10
в. 11
c. 12
D. 13
12
413For two events ( A ) and ( B, P(A cap B) ) is
This question has multiple correct options
( mathbf{A} cdot ) not less than ( P(A)+P(B)-1 )
B. not greater than ( P(A)+P(B) )
C . equal to ( P(A)+P(B)-P(A cup B) )
D・equal to ( P(A)+P(B)+P(A cup B) )
12
414The odds that a book will be reviewed
favourably by three independent critics are 5 to 2,4 to 3 and 3 to 4 respectively; what is the probability that of three reviews a majority will be favourable?
A ( cdot p=frac{149}{343} )
В. ( p=frac{209}{343} )
c. ( _{p}=frac{129}{3 frac{13}{33}} )
D. ( _{p}=frac{185}{343} )
12
415A die is thrown 200 times and the
outcomes 1,2,3,4,5,6 have
frequencies as below:
Outcome
Frequency
( begin{array}{llll}10 & 38 & 43 & 29end{array} )
Find the probabilities of getting a number more than 1 and less than 6 in a toss
(trial)
A . 0.65
в. 0.55
c. 0.69
D. None of these
12
416An urn contains 11 balls numbered from
to ( 11 . ) If a ball is selected at random,
what is the probabiloity of having a ball with a number which is mutliple of either 2 or ( 3 ? )
A ( cdot frac{7}{11} )
в. ( frac{8}{11} )
c. ( frac{4}{11} )
D. ( frac{6}{11} )
12
417Find probability of bag chosen out random contains more than ( 5 mathrm{kg} )
A . 0.7
B. 0.8
( c .0 .9 )
D. 0.6
12
418From three men and two women,
environment committee of two person to be formed.

Condition for event ( boldsymbol{A} ) : There must be at
least one woman member.
Condition for event ( B: ) One man, one
woman committee to be formed.
Condition for event ( C ) : There should not
be a woman member.

12
419A bag A contains 4 green and 6 red balls. Another bag B contains 3 green and 4 red balls. If one ball is drawn from
each bag, find the probability that both are green.
( A cdot 13 / 70 )
B. ( 1 / 4 )
( c cdot 6 / 35 )
D. 8/35
12
420If ( boldsymbol{P}(boldsymbol{A})=frac{4}{5} ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=frac{2}{5}, ) find
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
12
421A person is know to speak the truth 4
times out of ( 5 . ) He throws a die and
reports that it is a ace. The probability that it is actually a ace is
A. ( 1 / 3 )
в. 2 ( / 9 )
c. ( 4 / 9 )
D. ( 5 / 9 )
12
42219. A six faced fair dice is thrown until 1 comes, then the
probability that 1 comes in even no. of trials is (2005S)
(a) 5/11 (b) 5/6 (c) 6/11 (d) 1/6
12
423In a single toss of a coin the events ( {mathrm{H}} )
( {T} ) are mutually exclusive.
Write 1 if true and 0 if false
12
424A machine has fourteen identical
components that function
independently. It will stop working if three or more components fail. If the probability that a component fails is equal to ( 0.1, ) find the probability that the machine will be working.
12
425( A ) is a set containing ( n ) elements. subset ( P ) of ( A ) is chosen at random. The
set ( A ) is reconstructed by replacing the elements of the subset P.A subset Q of
A is again chosen at random. The probability that where ( |boldsymbol{X}|= ) number of elements in ( mathbf{X} )
12
426In a throw of coin, find the probability of getting a head.12
427Abag contains 6 white and an unknown
number of black balls ( (leq 3) ) Balls are
drawn one by one with replacement from this bag twice and is found to be white on both occasion. Find the
probability that the bag had exactly’ ( 3^{prime} )
Black balls.
12
428An unbiassed coins are tossed. Find the
probability of getting at most one head.
12
429Two numbers are selected at random
from integers 1 through ( 9 . ) If the sum is even, find the probability that both the
numbers are odd.
12
430Two aeroplanes I and II bomb a target in succession. The probabilities of I and I scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
в. ( frac{7}{22} )
( c .0 .2 )
D. 0.7
12
431A die having six faces is tossed 80 times and the data is as below:
outcome
[
begin{array}{ccc}
3 & 4 \
& \
& \
& \
10 & 28
end{array}
]
Frequency
( begin{array}{ll}20 & 0 \ 0 & 10 \ 2 & 0end{array} )
Find ( P(1) )
A. 0.175
в. 0.135
( c cdot 0.145 )
D. 0.125
12
432If ( bar{E} ) and ( overline{boldsymbol{F}} ) are the complementary
events of events ( boldsymbol{E} ) and ( boldsymbol{F} ) respectively
and if ( mathbf{0}<boldsymbol{P}(boldsymbol{F})<mathbf{1}, ) then:
This question has multiple correct options
( mathbf{A} cdot P(E / F)+P(bar{E} / F)=1 )
B cdot ( P(E / F)+P(E / bar{F})=1 )
C ( cdot P(bar{E} / F)+P(E / bar{F})=1 )
D ( cdot P(E / bar{F})+P(bar{E} / bar{F})=1 )
12
433A manufacturing firm produces steel pipes in three planet with daily production daily production of 500 1000 and 2000 units reespectively. According to past experience, it is known that the fraction of defective
output produced by the three planets are respectively ( 0.005,0.008,0.010 . ) if ( a ) pipe is selected from a day’s total production and faund to be defective,
find the probability that is has come
from the first plant
12
434( A ) speak the truth 8 times out of 10
times. A dice is tossed. He reports that
it was ( 5 . ) What is the probability that it was actually 5
12
435The probability that a student ( x )
participates in a competition is 0.4
while that for student ( y ) is ( 0.5 . ) The
probability that ( x ) participates in
competition, given that ( y ) also
participates is ( 0.7 . ) Then This question has multiple correct options
A. The probability that both ( x ) and ( y ) participates in that competition simultaneously is 0.35
B. The probability that ( y ) participates in that competition given that ( x ) also participates is ( frac{7}{8} )
C. The probability that atleast one of them participates in that competition is 0.55
D. The probability that exactly one of them participates in that competition is 0.20
12
436In a business venture a man can make
a profit of Rs. ( 2000 /- ) with probability of 0.4 or have a loss of Rs. ( 1000 /- ) with probability 0.6. His expected profit is
A. Rs. ( 800 /- )
B. Rs. ( 600 /- )
c. Rs. ( 200 /- )
D. Rs. 400/-
12
437Define event12
438A bag contains 3 red and 2 black balls. One ball is drawn from it at random.
Find the probability of drawing a red
ball.
12
439A game has 2 spinners. Spinner ( # 1 ) has a
probability of landing red of ( 2 / 3 . ) And, spinner#2 has a probability of landing red of ( 1 / 5 ) What is the probability spinner#1 lands red AND spinner#2 does NOT land red?
A . ( 2 / 15 )
B. ( 8 / 15 )
c. ( 13 / 15 )
D. 1
E. ( 3 / 5 )
12
440An unbiased cubical die whose faces
are numbered 1 to 6 is rolled once. Find
the probability of getting a square
number on the top face.
12
441If ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{boldsymbol{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} ) and
( P(bar{A} cap B cap bar{C})=frac{1}{3}, ) then what is
( boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) equal to?
A ( cdot frac{1}{12} )
B. ( frac{3}{4} )
c. ( frac{1}{15} )
D.
12
442A coin is tossed If it shows a tail we
draw a ball from a box which contains 2
red and 3 black balls If it shows head we
throw a die Find the sample space for this experiment
12
443Bag I contains 1 white, 2 black and 3 red
balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white,
3 black and 2 red balls. A bag is chosen
at random and two balls are drawn from
it with replacement. They happen to be one white and one red. What is the
probability that they came from Bag III.
12
444Any subset of sample space is called
A. event
B. probability
c. outcome
D. exprement
12
445If ( P(n o t A)=0.7, P(B)=0.7 ) and
( P(B / A)=0.5, ) find ( P(A bigcup B) )
12
446Define experiment12
447Check whether the probabilities ( boldsymbol{P}(boldsymbol{A}) )
and ( P(B) ) are consistently defined ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= )
( mathbf{0 . 6} )
12
448It is known that ( 60 % ) mice inoculated
with a serum are protected from a
certain disease. If 5 mice are
inoculated, find the probability that none contact the disease.
12
449Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. The variance of the number of aces is
A ( .24 / 169 )
B . ( sqrt{24 / 169} )
c. ( sqrt{24 / 173} )
D. ( 24 / 173 )
12
450If ( P(A)=frac{7}{13}, P(B)=frac{9}{13} ) and ( P(A cap )
( B)=frac{4}{13}, ) find ( P(A / B) )
12
451A die is thrown 400 times, the frequency of the outcomes of the events are given
as under.
outcome ‘ ( mathbf{3} ) 3. ( mathbf{2} ) 4
Frequency 70
65
60 1 75
Find the probability of occurrence of an odd number.
A ‘ the probability of occurrence of odd number ( =frac{5}{7} )
B. The probability of occurrence of odd number ( =frac{9}{2} )
C ‘ the probability of occurrence of odd number ( =frac{193}{400} )
D. The probability of occurrence of odd number ( =frac{200}{299} )
12
452Two unbiased coins whose faces are
marked 1 and 2 are tossed. The mean
value of the total of the numbers is
A . 3
B. 4
( c .5 )
D.
12
453Q Type your question
( y )
Development Houses
( 2 mathrm{Br} quad 3 mathrm{Br} quad 4 mathrm{Br} quad ) Total
single-Family ( 5 quad 19 quad 34 )
58
Townhouse
( 24 quad 42 quad 30 )
96
Total
( 29 quad 61 quad 64 )
A daycare centre is planning to distribute pamphlets to the families with children living houses with three or more bedrooms, due to budget. In addition to sending out flyers, it also decides to send out invitations for a free
day of daycare, to the family residing in two categories with the most houses. If
a house that already received a flyer is chosen at random to receive the second
stage of the marketing, then the probability that the house belongs to one of these two groups is ( frac{p}{q}, ) where ( p, q ) are co-primes.What is the value of ( boldsymbol{q}- )
( boldsymbol{p} ? )
12
454In the experiment of rolling a dice, find the probability of getting an even number that is multiple of 3.
A ( cdot frac{2}{5} )
B. ( frac{2}{3} )
( c cdot frac{3}{5} )
D. None of these
12
455Given two independence events ( A ) and
( B, ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
12
456There are 50 marbles of 3 colors: blue
yellow and black The probability of picking up a blue marble is ( 3 / 10 ) and that of picking up a yellow marble is ( 1 / 2 ) The probability of picking up a black ball is
A ( .1 / 5 )
B. 1/10
( c cdot 1 / 4 )
D. ( 4 / 5 )
12
457An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top
card is a red card.
12
458A symmetrical die is thrown four times and getting a multiple of 2 is considered to be a
success.
The mean and variance of success are
A ( cdot 4,2 )
в. 2,1
c. 0,2
D. 1,2
12
459When 2 dice are thrown simultaneously what is the probability that there is exactly one ( 5 ? )
A ( cdot frac{4}{36} )
в. ( frac{5}{18} )
c. ( frac{6}{23} )
D. ( frac{7}{24} )
12
460Given, ( P(A)=frac{3}{5} ) and ( P(B)=frac{1}{5} . ) Find
( P(A text { or } B), ) if ( A ) and ( B ) are mutually exclusive events.
12
461Every elementary event associated with a random experiment has probability12
462Suppose we have four boxes ( boldsymbol{A}, boldsymbol{B}, boldsymbol{C} )
and ( D ) containing colored marbles as
given :

One of the boxes has been selected at
random and a single marble is drawn
from it. If the marble is red, what is the
probability that it was drawn from box
( A, ) box ( B, ) box ( C ? )
begin{tabular}{cc|cc}
BOX & multicolumn{3}{c} { Marbles Color } \
hline & Red & White & Black \
hline ( mathrm{A} ) & 1 & 6 & 3 \
( mathrm{B} ) & 6 & 2 & 2 \
( mathrm{C} ) & 8 & 1 & 1 \
( mathrm{D} ) & 0 & 6 & 4 \
hline
end{tabular}

12
463There are three coins. One is a two-
headed coin another is a biased coin
that comes up heads ( 75 % ) of the time
and third is an unbiased coin. One of the
three coins is chosen at random and
tossed, it shows heads, what is the probability that it was the two-headed
coin?
12
464Out of 48 cricket matches between
India and England, India won toss 12 times. How many times England won
toss?
A . 12
B . 24
( c .36 )
D. 48
12
465The following is probabilty distribution
of r.v X.
[
begin{array}{lllllll}
mathbf{x} & 1 & 2 & 3 & 4 & 5 & 6 \
p(x) & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6} & frac{k}{6}
end{array}
]
then value of k is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
12
466Given two independent events ( A ) and ( B ) such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6 .} )
Find ( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}^{prime}right) )
12
467Let ( E^{c} ) denote the complement of an
event Let ( E, F, G ) be pairwise
independent events with ( P(G)>0 ) and
( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F} cap boldsymbol{G})=mathbf{0} operatorname{then} boldsymbol{P}left(boldsymbol{E}^{c} cap boldsymbol{F}^{c} mid boldsymbol{G}right) )
equals
( mathbf{A} cdot Pleft(E^{c}right)+Pleft(F^{c}right) )
B . ( Pleft(E^{c}right)-Pleft(F^{c}right) )
( mathbf{c} cdot Pleft(E^{c}right)-P(F) )
D. ( P(E)-Pleft(F^{c}right) )
12
468An unbiased die bearing the integers
-2 to 3 is thrown once
find the probability that the number drawn is,
A perfect square
12
469Let ( A ) and ( B ) be two events such that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) geq mathbf{3} / mathbf{4} ) and ( mathbf{1} / mathbf{8} leq boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B}) leq mathbf{3} / mathbf{8} )
Statement
1: ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B}) geq mathbf{7} / mathbf{8} )
statement
2: ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B}) leq 11 / 8 )
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1
B. Both the statements are TRUE and STATEMENT 2 is not the correct explanation of STATEMENT
c. STATEMENT1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE
12
470A bag contains 5 white and 7 black
balls; if two balls are drawn what is the
chance that one is white and the other
black?
12
471Suppose a machine produces metal parts that contain some defective parts
with probability ( 0.05 . ) How many parts should be produced in order that the probability of atleast one part being defective is ( frac{1}{2} ) or more?
(Given that, log ( _{10} 95=1.977 ) and
( left.log _{10} 2=0.3right) )
This question has multiple correct options
A . 11
в. 12
( c cdot 15 )
D. 14
12
472Three coins are tossed together Find,
The probability of getting no tail
12
473f 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains excatly 3
balls, is:
12
474In a simultaneous throw of a pair of dice, if the probability of getting neither 9 nor 11 as the sum of the numbers on the faces is ( frac{5}{a} . ) Find ( a )12
475A single letter is selected at random from the word’PROBABILITY’. The
probability that it is a vowel is:
A . ( 3 / 11 )
B. ( 4 / 11 )
c. ( 2 / 11 )
D.
12
476The range of a random variable ( boldsymbol{X} ) is
{0,1,2} and given that ( P(X=0)= )
( mathbf{3 c}^{3}, quad boldsymbol{P}(boldsymbol{X}=mathbf{1})=mathbf{4 c}- )
( mathbf{1 0 c}^{2}, quad boldsymbol{P}(boldsymbol{X}=mathbf{2})=mathbf{5} c-mathbf{1}, ) find (i)
the value of ( c )
(ii) ( boldsymbol{P}(boldsymbol{X}<mathbf{1}), quad boldsymbol{P}(1<boldsymbol{X} leq )
2) ( , quad P(0<X leq 3) )
12
477A bag contains 5 white, 7 red and 3
black balls. If a ball is chosen at random
Find the probability that it is not red.
12
478In a group of 950 persons, 750 can
speak Hindi and 460 can speak English.
Find how many can speak English only.
12
479A die is thrown:
( boldsymbol{P} ) is the event of getting an odd number
( Q ) is the event of getting an even number.
( R ) is the event of getting a prime
number.
Which of the following pairs is mutually exclusive?
A. ( P, Q )
в. ( Q, R )
( c . P, R )
D. None of these
12
480Let ( X ) and ( Y ) be two random variables.
The relationship ( boldsymbol{E}(boldsymbol{X} boldsymbol{Y})=boldsymbol{E}(boldsymbol{X}) )
( boldsymbol{E}(boldsymbol{Y}) ) holds
A . Always
B. If ( E(X+Y)=E(X)+E(Y) ) is true
c. If ( X ) and ( Y ) are independent
D. If ( X ) can be obtained from ( Y ) by a linear transformation
12
481A family has two children. What is the
probability that both the children are boys, given that atleast one of them is a boy?
12
482Tell whether the following is certain to happen, possible can happen but not certain.

A die when tossed shall land up with 8 on top.

12
483The probability of an event A occurring
is 0.5 and of B occuring ( s 0.3 . ) If ( A ) and ( B ) are mutually exclusive events, then the probability of neither A nor B occurring is
A . 0.6
B. 0.5
( c .0 .7 )
D. none of these
12
484In a school, there are 1000 students, out
of which 430 are girls. It is known that out of ( 430,10 % ) of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that chosen student is a girl?
12
485A random variable ( boldsymbol{X} ) has the following probability distribution:
[
begin{array}{lcccc}
begin{array}{l}
text { Values } \
text { of } mathbf{X}:
end{array} & -2 & -1 & 0 & 1 \
hline P(x): & 0.1 & mathrm{k} & 0.2 & 2 mathrm{k} \
& & & & \
& P(x): & & &
end{array}
]
Find the value of ( a, ) if ( k=frac{1}{a} )
12
486A discrete random variable X has the
probability distribution given below:
( x= )
1 0.5 1.5
2
( P(x): ) ( k ) ( 3 k ) ( 2 k ) The
Find the value of ( mathrm{k} )
12
487Compute ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}), ) if ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 2 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 8} )
( P(B)=0.25 )
12
488Define random experiment12
489Suppose ( A ) and ( B ) are independent events with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7} )
.Then compute:
a) ( P(A cap B) )
b) ( P(A cup B) )
( mathbf{c}) boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) )
d) ( Pleft(A^{c} cap B^{c}right) )
12
490Cards marked with numbers 4 to 99 are
placed in a box and mixed thoughtly. One card is drawn from this box. Find
the probability that the number on the card is a perfect square between 91 and
( mathbf{9 9} )
12
491The table gives the probability distribution of a random variable ( boldsymbol{X} )
[
begin{array}{lll}
x & 1 & 2 \
P(X= & &
end{array}
]
( x) )
0.2 0.1
[
begin{array}{ll}
0.3 & 0.3
end{array}
]
(i) Find ( P )
(ii) Find the mean of ( boldsymbol{X} )
(iii) Find the variance of ( boldsymbol{X} )
12
492Three coins are tossed. Describe two
events ( A ) and ( B ) which are mutually
exclusive.
12
493The probability of student ( A ) passing an examination is ( 2 / 9 ) and of students, ( B ) passing is ( 5 / 9 . ) Assuming the two events: ( A ) passes’. ( B ) passes’ as independent, find the probability of only
( B ) passing the examination
12
494Toss a coin for number of times as
shown in the table. And record your findings in the table.

Number of heads heads
10
[
begin{array}{l}
20 \
30
end{array}
]
40
50
What happens if you increase the
number of tosses more and more.

12
495Two balls are drawn at random with
replacement from a box containing 10 black and 8 red balls. Find the
probability that both balls are red
12
496A coin is tossed and a die is thrown
simultaneously :
( P ) is the event of getting head and a odd
number.
( Q ) is the event of getting either ( H ) or ( T )
and an even number.
( R ) is the event of getting a number on
die greater than 7 and a tail.
( S ) is the sample space.
Which of the following options is
correct?
A ( . n(S)=12, n(P)=3, n(Q)=2, n(R)=0 )
В. ( n(S)=12, n(P)=3, n(Q)=3, n(R)=0 )
c. ( n(S)=12, n(P)=3, n(Q)=6, n(R)=0 )
D. ( n(S)=12, n(P)=3, n(Q)=5, n(R)=0 )
12
497If a leap year is selected at random,
what is the chance that it will contain
53 tuesdays?
12
498In a group of 1000 people, there are 750
people who can speak Hindi and 400 who can speak English. Then number of persons who can speak Hindi only is
A . 300
в. 400
c. 600
D. None of these
12
499If ( A ) and ( B ) are two events in a sample
space ( S ) such that ( P(A) neq 0 ) and
( boldsymbol{P}(boldsymbol{B}) neq boldsymbol{0}, ) then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
A ( cdot P(A) cdot P(B) )
в. ( P(A) . Pleft(frac{B}{A}right) )
( mathbf{c} cdot P(B) )
D cdot ( P(A) )
12
500Given that she does not achieve
success, the chance she studied for 4
hour, is
A ( cdot frac{18}{26} )
в. ( frac{19}{26} )
c. ( frac{20}{26} )
D. ( frac{21}{26} )
12
501Verify that the following function can be regarded as p.d.f for the random
variable ( boldsymbol{X} )
-1 begin{tabular}{r}
1 \
hline
end{tabular} ( mathbf{0} )
1
( P(x) )
-0.2 0.2
12
502produced by a sleep researcher studying the number of dreams people
recall when asked to record their
dreams for one week. Group ( boldsymbol{X} )
consisted of 100 people who observed
early bedtimes, and Group ( Y ) consisted
of 100 people who observed later
bedtimes. If a person is chosen at
random from those who recalled at least
1 dream, what is the probability that the
person belonged to Group ( Y ? )
Dreams Recalled during One Week begin{tabular}{|l|c|c|c|c|}
hline & None & 1 to 4 & 5 or more & Total \
hline hline Group X & 15 & 28 & 57 & 100 \
hline Group Y & 21 & 11 & 68 & 100 \
hline Total & 36 & 39 & 125 & 200 \
hline
end{tabular}
( A )
( frac{68}{100} )
B. ( frac{79}{100} )
( c )
( frac{79}{164} )
D. ( frac{16}{text { ? }} )
12
503Marks in an aptitude test given to 800 students of a school was found to be
normally distributed. 10% of the
students scored below 40 Marks and
( 10 % ) of the students scored above 90
marks. Find the number of students
who scored between 40 and 90
12
504The probability of an event that cannot happen is ( _{–}-_{-} ? )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
( D )
12
505Find the probability that a number selected at random from the numbers 3
( 4,5, dots, 25 ) is prime
12
506If ( A ) and ( B ) are independent events of ( a ) random experiment such that ( P(A cap B)=frac{1}{6} ) and ( P(bar{A} cap bar{B})=frac{1}{3} )
then ( boldsymbol{P}(boldsymbol{A})= )
A ( cdot frac{1}{4}, frac{1}{3} )
B. ( frac{1}{2}, frac{1}{3} )
c. ( frac{1}{2}, frac{1}{5} )
D. ( frac{2}{3}, frac{1}{5} )
12
507A number is chosen at random from
among the 1 st 50 natural numbers. The probability that the number chosen is either a prime number or a multiple of 5 is
A ( cdot frac{12}{25} )
B. ( frac{1}{2} )
c. ( frac{14}{25} )
D.
12
508Find the number of ways of permuting the letters of the word PICTURE so
that
(i) All vowels come together
(ii) No two vowels come together
(iii) The relative positions of vowels and consonants are not disturbed
12
509An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are 2: 1 and the odds in favor of the
price remaining the same are ( 1: 3 . ) The probability that the price of the stock will go down during the next week, is
A ( cdot frac{4}{12} )
в. ( frac{5}{12} )
( c cdot frac{7}{12} )
D. none of these
12
510Three coins are tossed. Describe two
events ( A ) and ( B ) which are mutually
exclusive but not exhaustive.
12
511A random variable ( X ) has the
probability distribution ( X=x: )
( begin{array}{llllllll}1 & , 2 & , 3 & , 4 & , 5 & , 6 & , 7 & , 8end{array} )
( boldsymbol{P}(boldsymbol{X}) )
( mathbf{0 . 1 5}, mathbf{0 . 2 3}, mathbf{0 . 1 2}, mathbf{0 . 1}, mathbf{0 . 2}, mathbf{0 . 0 8}, mathbf{0 . 0 7}, mathbf{0 . 0 5} )
Events ( boldsymbol{E}={mathrm{X} text { is a prime number }} ) and
( boldsymbol{F}=boldsymbol{X} / boldsymbol{X}<mathbf{4} )
( boldsymbol{i}: boldsymbol{p}(boldsymbol{E} cup boldsymbol{F})=mathbf{0 . 2 3} )
( boldsymbol{i} boldsymbol{i}: boldsymbol{p}(overline{boldsymbol{E}} cup overline{boldsymbol{F}})=mathbf{0 . 6 5} )
Which of ( I, I I ) is (are) true?
A. I only
B. II only
c. both ( I ) and ( I I )
D. neither I nor ( I I )
12
512If the probabilities of the events ( boldsymbol{A} cap )
( B, A, B ) and ( A cup B ) are in A.P.with
second term of A.P. is equal to common difference then ( A ) and ( B ) are
A. independent
B. equally likely
c. mutually exclusive
D. can’t be determined
12
513In a school, ( 14 % ) of students take computer classes and ( 67 % ) take drama classes.What is the probability that a
student neither takes computer class nor takes drama class?
A ( frac{8}{100} )
в. ( frac{29}{100} )
c. ( frac{53}{100} )
D. ( frac{19}{100} )
12
51422. Consider 5 independent Bernoulli’s trials each with
probability of success p. If the probability of at least one
31
failure is greater than or equal to
then p lies in the
interval
[2011]
12
515An urn contains one black ball and one
green ball. A second urn contains one
white and one green ball. One ball is
drawn at random from each urn.Find the
probability of getting at least one green ball.
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{2}{3} )
D.
12
516Given two independent events ( A, B )
such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} )
Determine
( boldsymbol{P}(boldsymbol{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{B}) )
12
517The probability that Raju arrives on
time at school is 0.72
Write down the probability that he will
not arrive on time.
12
518Five defective mangoes are accidently
mixed with 15 good ones. Four mangoes
are drawn at random from this lot. Find
the probability distribution of the number of defective mangoes.
12
519( A ) bag ( X ) contains 4 white balls and 2
black balls, while another bag ( boldsymbol{Y} )
contains 3 white balls and 3 black balls
Two balls are drawn (without
replacement) at random from one of the bags and were found to be one white
and one black. Find the probability that the balls were drawn from bag ( Y )
12
520Bag A contains 2 red and 3 black balls
while another bag ( mathrm{B} ) contains 3 red and
4 black balls. One ball is drawn at
random from one of the bag and it is
found to be red. Find the probability that it was drawn from bag B.
12
521The probability of getting number less than or equal to ( 6, ) when a die is thrown once, is
A. An impossible event
B. A sure event
c. An exhaustive event
D. A complementary event
12
522The probabilities of three events ( A, B, C ) are events such that ( P(A)= ) ( mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{C})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B})=mathbf{0 . 0 8}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})=mathbf{0 . 2 8}, boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 0 9 .} ) If ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C}) geq mathbf{0 . 7 5} )
Show that ( P(B cap C) ) lies in the
interval [0.23,0.48]
12
523A bag contains 4 red and 5 black balls, a second bag contain 3 red and 7 black
balls. One ball is drawn at random from
each bag, find the probability that the
ball are of the same colour.
12
524There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random
from the box and if ( A ) is the event that
the number on the ticket is a multiple
of five, write the sample space ( boldsymbol{S}, boldsymbol{n}(boldsymbol{S}) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) )
12
525If coefficients ( a, b, c ) of quadratic equation ( a x^{2}+b x+c=0 ) are chosen
at random with replacement from the ( operatorname{set} S=1,2,3,4,5,6, ) find out the
probability that roots of quadratic are real and distinct.
A ( frac{20}{108} )
в. ( frac{19}{108} )
c. ( frac{21}{108} )
D. ( frac{22}{108} )
12
526A die is thrown 100 times and outcomes
are noted as given below:
Outcome: 1 3 4
Frequency:
( begin{array}{llll}21 & 9 & 14 & 23end{array} )
If a die is thrown at random, find the probability of getting a/an. 5
12
52716.
Two numbers are selected randomly from the set S={1,2,3
4, 5, 6} without replacement one by one. The probabilité
that minimum of the two numbers is less than 4 is (20035
(a) 1/15 (b) 14/15 (c) 1/5 (d) 4/5
10
528A pair of fair coins is tossed yielding the equiprobable space ( mathrm{S}={mathrm{HH}, mathrm{HT}, mathrm{TH}, mathrm{TT}} )
Consider the events:
( A={text { head on first } operatorname{coin}}={mathrm{HH}, mathrm{HT}} )
( mathrm{B}={text { head on second coin }}={mathrm{HH}, mathrm{TH}} )
( mathrm{C}={text { head on exactly one coin }}={mathrm{HT}, mathrm{TH}} )
Then check whether ( A, B, C ) are
independent or not.
12
529For three events ( A, B ) and ( C, P ) (Exactly
one of ( boldsymbol{A} text { or } boldsymbol{B} text { occurs })=boldsymbol{P}( ) Exactly one
of ( B text { or } C text { occurs })=P(text { Exactly one of } C ) or ( A text { occurs })=frac{1}{4} ) and ( P( ) All the three
events occur simultaneously) ( =frac{1}{16} )
Then the probability that at least one of the events occurs, is.
A ( cdot frac{7}{32} )
в. ( frac{7}{16} )
c. ( frac{7}{64} )
D. ( frac{3}{16} )
12
530A bag contains 5 white, 7 red and 3
black balls. If a ball is chosen at
random, then find the probability that it
is not red.
12
531One die of red colour one of white colour
and one of blue colour are placed in a
bag. One die is selected at random and rolled
its colour and the number on its
uppermost face is noted. Describe the
sample space
12
532The probability of an event ( k ) is
A ( .0 geq P(k) geq 1 )
в. ( 0 leq P(k) leq 1 )
c. ( 0>P(k)>1 )
D. ( 0<P(k)<1 )
12
533The time taken to assemble a car in a
certain plant is a random variable having a normal distribution of 20
hours and a standard deviation of 2
hours. What is the probability that a car can be assembled at this plant in a
period of time between 20 and 22
hours?
A . 0.3513
B. 0.3216
c. 0.3413
D. 0.3613
12
534A letter is taken out at random from the
word ASSISTANT and an other from
STATISTICS. The probability that they
are the same letters is
A ( cdot frac{13}{90} )
в. ( frac{17}{90} )
c. ( frac{19}{90} )
D. ( frac{15}{90} )
12
535If ( mathrm{m} / mathrm{n} ), in lowest terms, be the
probability that a randomly chose
positive divisor of ( 10^{99} ) is an integral
multiple of ( 10^{88} ) than find the value of
( (boldsymbol{m}+boldsymbol{n}) )
12
536A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black
balls. One of the two bags is selected at random and a ball is drawn from the
bag which is found to be red. Find the probability that the ball is drawn from the first bag.
12
537The probability of a sure event (or certain event) is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
( D )
12
538If 12 persons are seated at a round
table, what is the probability that two particular persons sit together?
A ( .2 / 11 )
B. 1/11
c. ( 1 / 12 )
D. ( 5 / 12 )
12
539If ( * ) represents 5 balloons then number
of symbols to be drawn to represent 60 balloons is
( mathbf{A} cdot mathbf{5} )
B. 60
c. 10
D. 12
12
540A box contain 10 red balls, 20 yellow balls and 50 blue balls. If a ball is drwan
at random from the box, find the probability that it will be
(i) a blue ball
(ii) neither yellow nor
blue
12
541Form 2 digit number using 0,1,2,3,4,5 without repeating the digits. Write the
sample space ( S, ) number of sample points ( n(S), U, n(U) ) for ( U ) is the event that the number so formed is divisible
by 5
12
54219 boys turn out for baseball. Of these
11 are wearing baseball shirts and 14 are wearing baseball pants. There are no boys without one or the other. The
number of boys wearing full uniform is
( mathbf{A} cdot mathbf{8} )
B. 6
c. 5
D. 3
12
543A speaks truth in ( 75 % ) of the cases and ( mathrm{B} ) in ( 80 % ) of the cases. In what
percentage of cases are they likely to
contradict each other in stating the same fact?
12
544f ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{B} / boldsymbol{A})= )
0.6. Find ( P(A / B) )
12
545A baised coin with probability ( boldsymbol{p}(mathbf{0}< )
( p<1) ) of heads is tossed until a head
appears for the first time. If the probability that the number of tosses required is even is ( frac{2}{5}, ) find ( 3 p )
12
546In a city, three daily newspapers ( A, B, C ) are published. ( 42 % ) of the people in that city read ( A, 51 % ) read ( B ) and ( 69 % ) read ( C .30 )
( % ) read ( A ) and ( B ; 28 % ) read ( B ) and ( C ; 36 % )
read ( A ) and ( C ; 8 % ) do not read any of the
three newspapers. The percentage of persons who read all the three papers is
A . ( 25 % ) %
B. 18%
c. ( 20 % )
D. none of these
12
547Three boxes numbered I, II, III contains
the balls as follows:
( begin{array}{llll}text { White } & text { Black } & text { Red } \ text { I } & 1 & 2 & 3 \ text { II } & 2 & 1 & 1 \ text { “II } & 4 & 5 & 3end{array} )
One box is randomly selected and a ball is drawn from it. If the ball is red, then
find the probability that it is from box II
12
548A fair coin is tossed four times and a
person win Re 1 for each head and lose
Rs. 1.50 for each tail that turns up. Let ( p ) be the probability of person losing Rs 3.50 after 4 tosses.Find ( 4 p ? )
12
549The geometric mean of the observations 2,4,8,16,32,64 is
A ( cdot 2^{5 / 2} / 2 )
2) 1
B ( cdot 2^{7 / 2} )
( c cdot 33 )
D. None of these
12
550Let ( X ) denote the number of hours you
study during a randomly selected school day. The probability that ( X ) can
take the value ‘x’ has the following from, where ‘k’ is some unknown constant.
( p=(X=X)= )
( left{begin{array}{ll}mathbf{0 . 1}, & boldsymbol{i f} boldsymbol{x}=mathbf{0} \ boldsymbol{k} boldsymbol{x}, & boldsymbol{x}=mathbf{1} boldsymbol{o r} mathbf{2} \ boldsymbol{k}(mathbf{5}-boldsymbol{x}), & boldsymbol{i f} boldsymbol{x}=mathbf{3} boldsymbol{o r} mathbf{4} \ mathbf{0}, & text { otherwise }end{array}right. )
(a) find the value of ‘k’
(b) what is the probability that you study :
(i) at least two hours?
(ii) exactly two hours??
(iii) at most 2 hours?
12
551The probability that certain electronic component fails when first used is 0.10 If it does not fail immediately, the probability that is lasts for one year is 0.99. The probability that a new component will last for one year is
A. 0.891
1
B. 0.692
( c cdot 0.92 )
D. None of these
12
552In a class of 100 students, 55 students
have passed in Mathematics and 67 students have passed in physics. Then the number of students who have
passed in physics only is
A . 22
B. 33
c. 10
D. 45
12
553The event which cannot happen is
called
A . outcome
B. impossible event
c. frequency
D. none of these
12
554A fair die is rolled. Consider the events
( boldsymbol{E}={1, mathbf{3}, mathbf{5}} ) and ( boldsymbol{F}={mathbf{2}, mathbf{3}}, ) find
( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) )
12
555Suppose an integer from 1 through 100 is chosen at random, find the
probability that the integer is a multiple of 2 or a multiple of 9
12
556If ( P(C)=frac{2}{7}, ) then ( P(bar{C})= )
A
B. ( frac{2}{7} )
c. 0
D.
12
557Define a simple event.12
558Least number of times must a fair die
be tossed in order to have a probability of at least ( 91 / 216 ), of getting atleast
one six.
12
559Find the probability that one will get 75 marks in the question paper of 100 marks.
A ( cdot frac{1}{101} )
в. ( frac{75}{100} )
c. ( frac{1}{100} )
D. ( frac{75}{101} )
12
560Lot ( A ) consists of ( 3 G ) and ( 2 D ) articles.
Lot ( B ) consists of ( 4 G 1 D ) article. A new
lot ( C ) is formed by taking 3 articles from ( A ) articles from ( A ) and 2 form ( B ). The
probability that an article chosen at random from ( C ) is
A . ( 1 / 3 )
в. 2 /
c. ( 8 / 25 )
D. none
12
561The average length of time required to complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 35 and 45 minutes to complete the questionnaire?
A. About ( 68 % )
B. About ( 72 % )
c. About ( 76 % )
D. About ( 84 % )
12
562A random variable ( X ) has the following probability distribution
[
begin{array}{llll}
boldsymbol{X}= & -2 & -1 & 0
end{array}
]
[
begin{array}{c}
P(x) \
text { Then } boldsymbol{E}(boldsymbol{x})=
end{array}
]
( begin{array}{llll}0.1 & 0.2 & 0.2end{array} )
A . 0.8
в. 0.9
c. 0.7
D. 1.
12
563From a pack of 52 cards, face cards and tens are removed and kept aside, then a card is drawn at random from the
remaining cards. If A: The events that the card is drawn is an ace. H: The
events that the card is drawn is a
heart.S: the events that the card is
drawn is a spade. Then, which of the following holds?
( mathbf{A} cdot 9 P(A)=4 P(H) )
B. ( P(S)=4 P(A cap H) )
c. ( 3 P(H)=P(A cap S) )
D. None of these
12
564A die is thrown. ( A ) is the event that
prime number comes up, ( B ) is the event
that the number divisible by three comes up, ( C ) is the event that the
perfect square number comes up. Then, ( A, B ) and ( C ) are :
A. Mutually exclusive
B. Mutually exhaustuve
c. Same
D. None of these
12
565In a certain town, ( 40 % ) of the people have
brown hair, ( 25 % ) have brown eyes and 15 ( % ) have both brown hair and brown eyes.
If a person selected at random from the town has brown hair, the probability that he also has brown eyes is
A . ( 1 / 5 )
B. 3/8
( c cdot 1 / 3 )
D. ( 2 / 3 )
12
566There are 40 students in a class and
their results is presented as below:
Result (Pass/Fail) Pass Fail
Number of Students 30
If a student chosen at random out of the
class, find the probability that the student has passed the examination
A . 0.12
B. 0.36
c. 0.65
D. 0.75
12
567There are 30 tickets numbered from 1 to
30 in a box and a ticket is drawn at
random. If ( A ) is the event that the
number on the ticket is a perfect
square, then write the sample ( S, n(S) ) the event ( boldsymbol{A} ) and ( boldsymbol{n}(boldsymbol{A}) )
12
568A die has 6 faces marked by the given numbers as shown below:
The die is thrown once. What is the
probability of getting the smallest integer?
( 1 3 longdiv { 2 3 } )
12
569In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in Hindi and Mathematics but not in
English?
A . 18
в. 12
( c cdot 10 )
( D )
12
570Let ( U=R( ) the set of all real numbers ) If
( A={x: x in R, 0<x<2}, B= )
( {x: x in R, 1<x leq 3} ), then
A. ( A cup B={x: x in R text { and } 0<x leq 3} )
B. ( A cap B={x: x in R text { and } 1<x<2} )
c. ( A-B={x: x in R text { and } 0<x leq 1} )
D. all of these
12
571If ( A ) and ( B ) are mutually exclusive
events, then
A ( . P(A)=P(A-B) )
B . ( P(B)=P(A-B) )
c. ( P(A)=P(A cap B) )
D. ( P(B)=P(A cap B) )
12
572A survey of 850 students in a University yields that 680 students like music and
215 like dance. What is the least
number of students who like both
music and dance?
A . 40
B . 45
c. 50
D. 55
12
573A die is thrown. Let ( A ) be the event that
the number obtained is greater than 3
Let ( mathrm{B} ) be the event that the number
obtained is less than 5. Then ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
is
A . 1
B. ( frac{2}{5} )
c. ( frac{3}{5} )
D.
12
574In a large metropolitan area, the probabilities are 0.87,0.36,0.36,0.30
that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or
both kinds of sets. What is the
probability that a family owns either any one or both kinds of sets?
12
575A garage mechanic keeps a box of good springs to use as replacements on
customers cars. The box contains 5
springs. A colleague, thinking that the springs are for scrap, tosses three faulty springs into the box. The mechanic picks two springs out of the box while servicing a car. Find the probability that the second spring drawn is faulty.
A ( cdot frac{1}{8} )
B. ( frac{2}{8} )
( c cdot frac{3}{8} )
D. ( frac{4}{8} )
12
576Four digit numbers are formed using
each of the digits ( 1,2, ldots ldots ., 8 ) only once One number from them is picked at random then the probability that the selected number contains unity is
A ( cdot frac{1}{2} )
B. ( frac{1}{8} )
( c cdot frac{1}{4} )
D. ( frac{1}{3} )
12
577If ( A ) is any event in a sample space then ( Pleft(A^{prime}right) ) is
( A cdot P(A) )
B. ( 1+P(A) )
c. ( 1-P(A) )
D. 1-2P(A)
12
578In 5 throws of a die, getting 1 or 2 is a success. The mean number of
successes is
A ( cdot frac{5}{3} )
в. ( frac{3}{5} )
( c cdot frac{5}{9} )
D. ( frac{9}{5} )
12
57912.
In a school only 3 out of 5 students can participate in a
competition
What is the probability of the students who do not make it
to the competition?
11
11
580There are 6 letters and 3 post-boxes. The number of ways in which these letters can be posted is
A ( cdot 6^{3} )
B . ( 3^{6} )
( mathrm{c} cdot^{6} C_{3} )
D. ( ^{6} P_{3} )
12
581If ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and
( Pleft(frac{B}{A}right)=0.4 ) then ( Pleft(frac{A}{B}right)=? )
A .0 .32
B. 0.64
c. 0.16
D. 0.25
12
582The experiment is to repeatedly toss a coin until first tail shows up. Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these
12
583A prisoner escapes from a jail and is equally likely to choose one of the four roads I, II, III or IV to reach away from the hands of law. If he choose I road, he is successful with probability ( 1 / 6 ) and for
I, III and IV this is ( 1 / 8,1 / 10 ) and ( 1 / 12 ). If the prisoner is successful, the probability that he chose road
12
584Four persons can hit a target correctly with probabili
1 1
23 and respectively. If all hit at the target indepe
dently, then the probability that the target would be hit,
JEEM 2019-9 April (M
(a)
25
12
585( boldsymbol{P}(boldsymbol{A})=mathbf{3} / mathbf{8} ; boldsymbol{P}(boldsymbol{B})=mathbf{1} / mathbf{2} ; boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
( mathbf{5} / mathbf{8}, ) which of the following do/does hold
good? This question has multiple correct options
A ( cdot Pleft(A^{C} / Bright)=2 Pleft(A / B^{C}right) )
B . ( P(B)=Pleft(A^{C} / Bright) )
C ( cdot 15 Pleft(A^{C} / B^{C}right)=8 Pleft(B / A^{C}right) )
D ( cdot Pleft(A / B^{C}right)=(A cap B) )
12
586Two dice are thrown at a time, find the
probability that the sum obtained is
less than 6
( A cdot frac{2}{9} )
B. ( frac{1}{4} )
c. ( frac{5}{18} )
D. ( frac{1}{3} )
12
58715.
If the integers m and n are chosen at random from 1 to 100
then the probability that a number of the form 7m + 7nic
divisible by 5 equals
(1999 – 2 Marks)
(a 1/4 (b) 1/7 (c) 1/8 (d) 1/49
21.
a
(1
11
588Three coins are tossed. Describe
two events ( A ) and ( B ) which are mutually
exclusive but not exhaustive.
12
589The odds against a certain event are 5 to 2 and the odds in a fvour of another
event independent to the former are 6 to
5. Find the probability that none of the events will occur.
12
590A, ( mathrm{B} ) are two inaccurate arithmeticians
whose chances of solving a given question correctly are ( (1 / 8) ) and ( (1 / 12) ) respectively. They solve a problem and obtained the same result. If it is 1000 to
1 against their making the same mistake, find the chance that the result
is correct
( mathbf{A} cdot frac{13}{14} )
B. ( frac{2}{7} )
( c cdot frac{1}{8} )
D. ( frac{11}{12} )
12
591If ( X ) follows a binomial distribution with
parameters ( n=100 ) and ( P=frac{1}{3}, ) then
( P(X=r) ) is maximum when ( r= )
A . 33
B. 50
c. 25
D. none of these
12
592( P ) makes a bet with ( Q ) of 8 pounds to
120 pounds that three races will be won by the three horses ( A, B, C, ) against which the betting is 3 to 2,4 to ( 1, ) and 2 to 1 respectively. The first race having been a on by ( A ), and it being known that
the second race was won either by ( B ), or
by a horse ( D ) against which the betting
was 2 to 1 , find the value of ( P^{prime} s )
expectation.
12
593A random variable ( X ) has the following
probability distribution:
[
begin{array}{cccccc}
boldsymbol{X} & mathbf{1} & mathbf{2} & mathbf{3} & mathbf{4} & mathbf{5} \
hline P(X) & k^{2} & 2 k & k & 2 k & 5
end{array}
]
[
5 k^{2}
]
Then ( P(X>2) ) is equal to
( mathbf{A} cdot frac{1}{6} )
B. ( frac{7}{12} )
c. ( frac{1}{36} )
D. ( frac{23}{36} )
12
594PTUU
10.
Three hous
Three houses are available in a locality. Three persons apply
for the houses. Each applies for one house without
consulting others. The probability that all the three apply
for the same house is
[2005]
(d)
12
59517.
A die is thrown
die is thrown. Let A be the event that the number obtained
eater than 3. Let B be the event that the number obtained
is less than 5. Then P(AUB) is
[2008]
(b) 0
(a)
5
(d) 2
11
596In a bolt factory, three machines ( A, B ) and ( C ) manufacture 25,35 and 40
percent of the total bolts respectively. Out of the total bolts manufactured by
the machines 5,4 and 2 percent are
defective from machine ( A, B & C )
respectively. A bolt is drawn at random and is found to be defective. Find the
probability that it was manufactured by
(i) Machine A or ( C )
(ii) Machine B.
12
597An unbiased die is thrown twice. Let the
even ( A ) be ( ^{prime} ) odd ( ^{prime} ) number on the first
throw and ( B ) the event ( ^{prime} ) odd number on
the second throw’. Check the
independence of the events ( A ) and ( B ).
12
598An instructor has a question bank
consisting of 300 easy True / False questions, 200 difficult True / False
questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question
bank, what is the probability that it will
be an easy question given that it is a multiple choice question?
12
599Supposing that it is 9 to 7 against a person A who is now 35 years of age living till he is ( 65, ) and 3 to 2 against a person B now 45 living till he is ( 75 ; ) find the chance that one at least of these
persons will be alive 30 years hence.
12
600A coin is tossed 100 times with
following frequency. Head : 25, Tail : 75
How many outcomes are possible here?
A. one
B. Two
c. three
D. Four
12
601Let the discrete random variable ( boldsymbol{X}=boldsymbol{x} )
has the probabilities given by ( frac{x}{6} ) for ( x= )
( 0,1,2,3, ) then its mean is
A ( cdot frac{1}{3} )
в. ( frac{5}{3} )
( c cdot frac{7}{3} )
D. ( frac{9}{3} )
12
602A box contains 10 white, 6 red and 10
black balls. A ball is drawn at random
from the box. What is the probability
that the ball drawn is either white or
red?
A ( cdot frac{7}{13} )
в. ( frac{7}{12} )
c. ( frac{8}{13} )
D. ( frac{9}{15} )
12
603Two number are selected at random
(without replacement ) from the first six positive integers. Let ( X ) denote the larger of the numbers obtained. Find ( E )
( (x) )
12
604If ( A ) is an event of a random experiment, then ( A^{C} ) or ( A^{-} ) or ( A^{prime} ) is called the
compliment of the event.
If true then enter 1 and if false then
enter 0
A. 0
B. Can’t determine
( c )
D. None of these
12
605If a letter is chosen at random from the
English alphabet, if the probability that the letter is a consonant is ( frac{a}{26}, ) then
what is the value of ( a ? )
12
606If ( boldsymbol{P}left(boldsymbol{E}_{boldsymbol{k}}right)=boldsymbol{C} ) for ( mathbf{0} leq boldsymbol{k} leq boldsymbol{n}, ) then ( boldsymbol{P}(boldsymbol{A}) )
equals
A ( cdot 1 / 2 )
в. ( 2 / 3 )
( c cdot 1 / 6 )
D. ( 1 /(n+1) )
12
607Une Indian and four American men and their wives are to be
seated randomly around a circular table. Then the conditional
probability that the Indian man is seated adjacent to his
wife given that each American man is seated adjacent to his
wife is
(2007 -3 marks)
(a)
(b)
(c) =
T
he 1
28.
12
608Two coins are tossed simultaneously. Find the probability that either both
heads or both tails occur
12
609( A ) and ( B ) are events with ( P(A)= ) ( mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 7} ) then compute ( boldsymbol{P}(boldsymbol{A} cap )
( B) )
12
610If ( A ) and ( B ) are independent events such that ( mathbf{0}<boldsymbol{P}(boldsymbol{A})<mathbf{1}, mathbf{0}<boldsymbol{P}(boldsymbol{B})<mathbf{1}, ) then
This question has multiple correct options
A. A, B are mutually exclusive
B. A and ( bar{B} ) are independent
c. ( bar{A} ) and ( bar{B} ) are independent
D. ( P(A / B)+P(bar{A} / B)=1 )
12
611A person goes to work by car, train or bus. The probabilities of person travelling by there modes are ( 3 / 10,1 / 2 ) and ( 1 / 5 ) respectively. It is found that chance of person being late for work are ( mathbf{3} / mathbf{7}, mathbf{1} / mathbf{7} ) and ( mathbf{5} / mathbf{7} ) by respective modes
Given that on particular day person reaches late, find the probability that on that day he had travelled by train
12
612A card is thrown from a pack of 52 cards
so that each cards equally likely to be selected. In which of the following cases are the events ( A ) and ( B ) independent?
( A= ) the card drawn is spade, ( B= ) the
card drawn in an ace.
12
613A box contains 6 red marbles numbers
from 1 through 6 and 4 white marbles
12 through 15. Find the probability that a marble drawn ‘at random’ is white and
odd numbered
A . 5
B. ( frac{1}{5} )
( c cdot 6 )
D.
12
614A card is drawn at a random from a
pack of 52 cards. What is the probability of drawing a king or a jack?
A . ( 1 / 52 )
в. 2/26
( c cdot 1 / 13 )
D. 2/13
12
615A die is rolled so that the probability of
face ( i ) is proportional to ( i,{i= ) ( 1,2, dots .6} . ) The probability of an even number occurring when the die is rolled
is
( A cdot frac{7}{4} )
B. ( frac{4}{7} )
( c cdot frac{5}{7} )
D. None of these
12
616Which one can represent a probability
of an event
A ( cdot frac{7}{4} )
B. – 1
c. ( -frac{2}{3} )
D. ( frac{2}{3} )
12
617A dice is thrown ( 2 n+1 ) times, ( n epsilon N )
The probability that faces with even numbers show odd number of times is
A ( cdot frac{2 n+1}{4 n+3} )
B. less than ( frac{1}{2} )
c. greater than ( frac{1}{2} )
D. none of these
12
618Three numbers are chosen at random
without replacement from ( 1,2,3, dots . ., 10 ) The probability that the minimum of
the chosen numbers is 3 or their
maximum is 7 is
A ( cdot 1 / 2 )
в. ( 1 / 3 )
c. ( 1 / 4 )
D. ( 11 / 40 )
12
619( X ) follows a binomial distribution with
parameters ( boldsymbol{n}=boldsymbol{6} ) and ( boldsymbol{P} . ) If ( boldsymbol{4} boldsymbol{P}(boldsymbol{x}= )
( mathbf{4})=boldsymbol{P}(boldsymbol{x}=mathbf{2}), ) then ( boldsymbol{P}= )
A ( cdot frac{1}{2} )
в.
( c cdot frac{1}{6} )
D.
12
620A die is rolled, find the probability that an odd numbers is obtained.
A ( cdot frac{1}{2} )
B. ( frac{3}{2} )
( c cdot frac{7}{2} )
D. ( frac{6}{3} )
12
621The sample space in the set
representing an event more than one element is called
A. compound
B. simple
c. impossible
D. complementary
12
622An urn contains 2 white and 2 black
balls. A ball is drawn at random. If it is
white it is not replaced into the urn. Otherwise it is along with another ball
of same colour. The process is repeated. the probability that the third ball drawn is black is a/b (no common divisor),
then ( b-a= )
12
623A person drawn a card from a pack of 52 cards, replaces it ( & ) shuffles the pack. He continues doing this till the draws a spade. The probability that he will fail exactly the first two times is
A ( cdot frac{1}{64} )
в. ( frac{9}{64} )
c. ( frac{36}{64} )
D. ( frac{60}{64} )
12
624A symmetric die is thrown ( (2 n+1) ) times. The probability of getting a prime score on the upturned face at most ( n )
times is
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{4} )
D.
12
625The probability of selecting a green marble at random from a jar that
contains only green, white and yellow marbles is ( 0.25 . ) The probability of selecting a white marble at random from the same jar is ( frac{1}{3} . ) If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?
12
626If from each of the three boxes containing 3 white and 1
black, 2 white and 2 black, 1 white and 3 black balls, one ball
is drawn at random, then the probability that 2 white and 1
black ball will be drawn is
(1998 – 2 Marks)
(a) 13/32 (b) 1/4 (c) 1/32 (d) 3/16
12
627If ( A ) and ( B ) are two events such that ( P(A cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq frac{3}{8} )
then
This question has multiple correct options
( ^{mathbf{A}} cdot P(A)+P(B) leq frac{11}{8} )
в. ( P(A) . P(B) leq frac{3}{8} )
c. ( P(A)+P(B) geq frac{7}{8} )
D. none of these
12
628Two aeroplanes ( I ) and ( I I ) bomb a target
in succession. The probability of ( boldsymbol{I} ) and
( I I ) scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
B. 0.14
c. 0.32
D. 0.7
12
629Two events ( A ) and ( B ) will be independent
if
( mathbf{A} cdot Pleft(A^{prime} cap B^{prime}right)=(1-P(A))(1-P(B)) )
B ( cdot P(A)+P(B)=1 )
( mathbf{c} cdot P(A)=P(B) )
D. ( A ) and ( B ) are mutually exclusive
12
630A bag contain 4 white, 7 black and 5 red
balls. A ball is drawn Find the
probability that the ball drawn is red.
12
631A problem in mathematics is given to 4 students whose chances of solving individually are ( frac{1}{2}, frac{1}{3}, frac{1}{4} ) and ( frac{1}{5} . ) The probability that the problem will be solved at least by one student is?
A ( cdot frac{2}{3} )
в. ( frac{3}{5} )
( c cdot frac{4}{5} )
D. ( frac{3}{4} )
12
632In a series of 3 one-day cricket matches between teams ( A ) and ( B ) of a college, the probability of team A winning or drawing are ( 1 / 3 ) and ( 1 / 6 ) respectively. If a
win, loss or draw gives 2,0 and 1 point
respectively, then what is the
probability that team A will score 5
points in the series?
A ( cdot frac{17}{18} )
B. ( frac{11}{12} )
( c cdot frac{1}{12} )
D. ( frac{1}{18} )
12
633If ( A ) and ( B ) are two events such that
( boldsymbol{P}(boldsymbol{A})=frac{1}{4}, boldsymbol{P}(boldsymbol{B})=frac{1}{2} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= )
( frac{1}{8} ) find ( P A cup B )
12
634Find the mean of the binomial distribution ( Bleft(4, frac{1}{3}right) )12
635Jiah is doing an experiment in her math class. She flips four coins in the air. What is most likely to happen?
A. Two of the coins will be heads and two will be tails
B. Three of the coins will be heads and one will be tail
c. All four coins will be heads
D. None of the coins will be heads
12
636If ( A ) and ( B ) are two events such that ( P(A cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq )
( mathbf{3} )
( overline{mathbf{8}}^{prime} )
then
This question has multiple correct options
A ( cdot P(A)+P(B) geq frac{7}{8} )
B . ( P(A)+P(B) leq 11 / 8 )
( c cdot P(A) P(B) leq frac{3}{8} )
D. None of these
12
637Which of the following experiments does NOT have equally likely outcomes?
A. Choose a number at random from 1 to 7
B. Toss a coin
c. choose a letter at random from the word school
D. None of the above
12
638State true or false:
The probabilities of three mutually
exclusive events ( A, B, C ) are ( P(A)= )
( frac{2}{3}, P(B)=frac{1}{4}, P(C)=frac{1}{6} )
A. True
B. False
12
639Events ( E_{1}, E_{2}, E_{3} ) are possible events of an experiment and their probabilities are recorded.Mark the possible correct
answers.
This question has multiple correct options
( begin{array}{ll}text { A } cdot Pleft(E_{1}right)=0.3, & Pleft(E_{2}right)=0.4, quad Pleft(E_{3}right)=0.3end{array} )
B – ( Pleft(E_{1}right)=0.1, quad Pleft(E_{2}right)=0.4, quad Pleft(E_{3}right)=0.5 )
C ( cdot Pleft(E_{1}right)=0.6, quad Pleft(E_{2}right)=-0.3, quad Pleft(E_{3}right)=0.7 )
D ( cdot Pleft(E_{1}right)=0.4, quad Pleft(E_{2}right)=0.2, quad Pleft(E_{3}right)=0.3 )
12
640post a letter to my friend and do not receive a reply. It is known that one letter out of ( m ) letters do not reach its
destination. If it is certain that my friend will reply if he receives the letter If ( A ) denotes the event that my friend receives the letter and ( B ) that I get a
reply, then This question has multiple correct options
A ( cdot P(B)=(1-1 / m)^{2} )
B . ( P(A cap B)=(1-1 / m)^{2} )
c. ( Pleft(A mid B^{prime}right)=(m-1) /(2 m-1) )
D. ( P(A cup B)=(m-1) / m )
12
641f ( A, B, C ) are three events show that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})+ )
( boldsymbol{P}(boldsymbol{C})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})-boldsymbol{P}(boldsymbol{b} cap boldsymbol{C})- )
( boldsymbol{P}(boldsymbol{C} cap boldsymbol{A})+boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}) )
12
642Three numbers are chosen at random
without replacement from ( {1,2, ldots, 8 .} )
The probability that their minimum is 3 given that their maximum is 6 is
A ( cdot frac{2}{5} )
B. ( frac{3}{8} )
( c cdot frac{1}{5} )
D.
12
643In a test an examinee either guesses or copies or knows the answer to a
multiple choice question with 4 choices. The probability that he makes a guess is ( frac{1}{3} ) and the probability that he copies the answer is ( frac{1}{6} . ) The probability
that his answer is correct given that he copied it, is ( frac{1}{8} . ) Find the probability that he knew the answer to the question
given that he correctly answered it.
A ( cdot frac{11}{29} )
B. ( frac{18}{29} )
c. ( frac{15}{29} )
D. ( frac{24}{29} )
12
644Cards marked with number 2 to 101 are
placed in a box and mixed thoroughly. One card is drawn from this box. Find
the probability that the number of the card is an even number
12
645Two integers are selected at random
from the set ( 1,2, ldots, 11 . ) Given that the sum of selected numbers is even, the
conditional probability that both the
numbers are even is:
A ( cdot frac{2}{5} )
B. ( frac{1}{2} )
( c cdot frac{3}{5} )
D. ( frac{7}{10} )
12
646A biased coin with probability ( P,(0<p< )
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is ( frac{2}{5} ) then ( P= )
( A cdot frac{2}{5} )
B.
( c cdot frac{2}{3} )
( D cdot frac{1}{3} )
12
647[
begin{array}{lllll}
X=x & -2 & -1 & 0 & 1 \
P(X= & 0.1 & K & 0.2 & 2 K
end{array}
]
( x) )
is the probability distribution of random variable ( X ). Find the value of ( K )
and variance of ( boldsymbol{X} )
12
648A market research group conducted a survey of 2,000 consumers and reported that 1720 consumers liked
product ( P_{1} ) and 1,4500 consumers liked
product ( P_{2} . ) What is the least number that must have liked both the products.
12
649There are ( m ) persons sitting in a row. two of them are selected at random. The
probability that the two selected persons are not together is ( 1-frac{2}{m} . ) If
true enter 1 else 0
12
6503 cards are given, one of them is red on both sides, one is blue on both sides ( & )
one is blue on one side red on the other
side. One of them is chosen randomly ( & ) put on the table. It shows red colour on
the upper side. The chance of the other
side of the card being red is:
12
651The probability that a leap year will have
only 52 Sundays is
A ( cdot frac{4}{7} )
B. ( frac{5}{7} )
( c cdot frac{6}{7} )
D.
12
652Assertion
If ( boldsymbol{B} subset boldsymbol{A}, ) then ( boldsymbol{P}(boldsymbol{A} cap overline{boldsymbol{B}})=boldsymbol{P}(boldsymbol{A})- )
( boldsymbol{P}(boldsymbol{B}) )
Reason
( (boldsymbol{A} cap overline{boldsymbol{B}}) cup boldsymbol{B}=boldsymbol{A} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
653In a box containing only purple and green marshmallows, 6 marshmallows
are purple. If the probability of choosing
a purple marshmallow from the box is ( frac{1}{3}, ) calculate the number of green marshmallows in the box.
( A cdot 2 )
B. 6
c. 9
D. 12
E . 18
12
654( X ) and ( Y ) are independent binomial ( operatorname{variates} boldsymbol{A}left(mathbf{5}, frac{mathbf{1}}{mathbf{2}}right) ) and ( boldsymbol{B}left(mathbf{7}, frac{mathbf{1}}{mathbf{2}}right) ) then
( boldsymbol{P}(boldsymbol{X}+boldsymbol{Y}=boldsymbol{3}) )
A ( cdot frac{45}{1024} )
в. ( frac{55}{1024} )
c. ( frac{65}{1024} )
D. ( frac{60}{1024} )
12
655For any two events ( A ) and ( B ) in a sample
space
This question has multiple correct options
( ^{mathbf{A}} cdot p(A / B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true
B . ( P(A cap B)=P(A)-P(bar{A} cap bar{B}) ) does not hold
C ( . P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( mathrm{A} ) and ( mathrm{B} ) are independent
D. ( P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( mathrm{A} ) and ( mathrm{B} ) are disjoint
12
656Sum of the probabilities of all the elementary events of an experiment is
( mathbf{A} cdot mathbf{0} )
B. 0.2
c. 1
D. 0.8
12
657( boldsymbol{8} boldsymbol{p}(overline{boldsymbol{A}} cap boldsymbol{B}) )12
658If the sum of the mean and variance of a
binomial distribution for 6 trials be
( 10 / 3, ) find the distribution.
12
659The probability of an even happens in one trial of an experiment is ( 0.3 . ) Three independent trials of the experiments are performed. Find the probability that the event A happens at least once.
A .0 .657
B. 0.965
c. 0.796
D. 0.509
12
660Weight ( 50-quad 56 )
(in ( mathrm{kg}) )
Number
of 15
students
Garima collected the data regarding
weights of students of her class and prepared the above table:
A student is to be selected randomly from her class for some competition.
The probability of selection of the
student is the highest whose weight (in
kg) is in the interval
A. ( 44-49 )
B. ( 56-61 )
c. ( 50-55 )
D. ( 62-67 )
12
661A purse contains 4 copper coins and 3
silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
A ( cdot frac{41}{70} )
B. ( frac{31}{70} )
c. ( frac{27}{70} )
D.
12
662From a well shuffled pack of 52 playing cards, four are drawn at random. The
probability that all are spades, but one is a king is:
( ^{mathrm{A}} cdot frac{39}{^{52} C_{4}} C_{4} )
в. ( frac{12}{52} C_{3} )
( ^{mathrm{C}}-frac{^{39} C_{4}}{^{52} C_{4}} )
D. ( frac{12}{52} C_{4} )
12
663A letter is known to have come from
either ( boldsymbol{T} boldsymbol{A} boldsymbol{T} boldsymbol{A} boldsymbol{N} boldsymbol{A} boldsymbol{G} boldsymbol{A} boldsymbol{R} ) or
CALCUTTA. On the envelope just two consecutive letters ( boldsymbol{T} boldsymbol{A} ) are visible. The
probability that the letter has come
from ( C ) ALCUTTA is
A ( cdot frac{4}{11} )
B. ( frac{1}{3} )
c. ( frac{5}{11} )
D. ( frac{4}{7} )
12
664Show that ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{A} cap boldsymbol{B} ) implies ( boldsymbol{A}= )
( boldsymbol{B} )
12
665In a batch of 10 articles, 4 articles are
defective. 6 articles are taken from the
batch for inspection If more than 2 articles in this batch are defective, the whole batch is rejected Find the
probability that the batch will be rejected.
12
666( mathbf{A} )
& B are sharp shooters whose probabilities of hitting a target are ( frac{mathbf{9}}{mathbf{1 0}} )
( & frac{14}{15} ) respectively. If it is knownthat exactly one of them has hit the target, then the probability that it was hit by ( A ) is equal to
A ( cdot frac{24}{55} )
в. ( frac{27}{55} )
c. ( frac{9}{23} )
D. ( frac{10}{23} )
12
667Which one of the following is an impossible event?

This question has multiple correct options
A. Rolling a die to get 4
B. Tossing a coin to get tail
c. choosing 4 face cards of spades.
D. Rolling a die for 7

12
668Define sure event.12
669Which experiment has equally likely outcomes?
A. Choose a number at random from 1 to 7
B. Toss a coin
c. Roll a die
D. All the above
12
670The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3: 2 . It is known that an average of one truck in thirty trucks and two cars in fifty cars
stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car
( A cdot frac{4}{9} )
в. ( frac{9}{250} )
( c cdot frac{3}{5} )
D. ( frac{1}{30} )
12
671A bag contain 8 red, 3 white and 9 blue
balls. If three balls are drawn at random,
determine the probability that all the three balls are blue balls
A ( cdot frac{7}{93} )
в. ( frac{6}{92} )
c. ( frac{7}{95} )
D. ( frac{8}{95} )
12
6724 normal distinguishable dice are rolled once. The number of possible outcomes in which at least one dice shows up 2?
A . 216
B. 648
c. 625
D. 67
12
673Two unbiased dice are thrown together
at random. Find the expected value of
the total number of points shown up.
12
674There are 4 balls of different colours ( & 4 )
boxes of colours same as those of the
balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is:
A . 9
B . 30
c. 20
D. None
12
675Two different dice are tossed together
Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10 , of the number on the two dice.
12
676Which of the following is an random
experiment?
This question has multiple correct options
A. Rolling a pair of dice
B. Choosing 2 marbles from a jar
C. Choosing a number at random from 1 to 10
D. Tossing two coins
12
67710. A coin is tossed 200 times and head appeared 120 times
The probability of getting a head in this experiment is
11
678The probability that a man will live 10 more years, is ( frac{1}{4} ) and the probability that his wife will live 10 more years, is
( mathbf{1} )
– Then, what is the probability that
( overline{mathbf{3}} )
neither will be alive in 10 years?
A ( cdot frac{1}{2} )
в. ( frac{3}{7} )
( c cdot frac{2}{3} )
D.
12
679A survey of people in a given region showed that ( 20 % ) were smokers. The
probability of death due to lung cancer, given that a person smoked, was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is ( 0.006, ) what is the probability of death due to lung cancer given that a person is a smoker?
A ( cdot 1 / 140 )
в. ( 1 / 70 )
( c cdot 3 / 140 )
D. ( 1 / 10 )
12
680If a random variable ( X ) takes value 0 and
1 with respective probabilities ( frac{2}{3} ) and ( frac{1}{3} ) then the expected value of ( X ) is
A ( cdot frac{2}{3} )
B. ( frac{1}{3} )
c. 0
D.
12
681If ( frac{2}{11} ) is the probability of an event.
What is the probability of the event ‘not
( boldsymbol{A}^{prime} )
12
682A black and a red die are rolled together. Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4
12
683A die is thrown 4 times. The probability of getting atmost two 6 is
( mathbf{A} cdot 0.984 )
B. 0.802
c. 0.621
D. 0.72
12
684If a selected student has been found to
pass the examination then find out the
probability that he is the only student to have passed the examination.
( ^{mathbf{A}} cdot_{Pleft(E_{1} / Aright)}=frac{4}{[n(2 n+1)]^{2}} )
в. ( quad Pleft(E_{1} / Aright)=frac{2}{[n(2 n+1)]^{2}} )
( ^{mathrm{c}} Pleft(E_{1} / Aright)=frac{4}{[n(n+1)]^{2}} )
D. ( quad Pleft(E_{1} / Aright)=frac{2}{[n(n+1)]^{2}} )
12
685Two dice each numbered from 1 to 6 are
thrown together. Let ( A ) and ( B ) be two
events given by
( A: ) even number on the first die
( B: ) number on the second die is greater
than 4
Find the value of ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
A ( cdot frac{1}{2} )
B. ( frac{1}{4} )
( c cdot frac{2}{3} )
D. ( frac{1}{6} )
12
686A die is thrown thrice. Find the
probability of getting an odd number
number at least once.
12
687Two symmetrical dice are thrown. The probability of getting a sum of 6 points
is
A ( cdot frac{4}{36} )
в. ( frac{5}{36} )
c. ( frac{6}{36} )
D. ( frac{1}{36} )
12
688There are three events ( A, B, C ) one
which must and only one can happen; the odds are 8 to 3 against ( A, 5 ) to 2
against ( B . ) The odds against ( C ) is 43:
17k. Find the value of ( k ) ?
12
689The probability distribution function of a random variable ( boldsymbol{X} ) is given by
( boldsymbol{x}_{i}: quad 0 quad 1 quad 2 )
( c / 2 quad c quad 2 c )
where ( c>0 . ) Find ( c )
12
690When a dice is thrown, find the
probability that either an odd number or a multiple of 4 occurs
12
691Which of the following is not true regarding the normal distribution?
A. the point of inflecting are at ( X=mu pm sigma )
B. skewness is zero
c. maximum heigth of the curve is ( frac{1}{sqrt{2 pi}} )
D. mean = media = mode
12
692If ( A ) and ( B ) are two events then
This question has multiple correct options
( mathbf{A} cdot P(A cap B) geq P(A)+P(B)-1 )
B ( . P(A cap B) geq P(A)+P(B) )
( mathbf{c} cdot P(A cap B)=P(A)+P(B)-P(A cup B) )
( mathbf{D} cdot P(A cap B)=P(A) cdot P(B) )
12
693f ( P(A)=0.40, P(B)=0.35 ) and
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 5 5}, ) then ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})= )
( A )
5
B. ( frac{8}{11} )
( c cdot frac{4}{7} )
D.
12
694An urn contains 3 white and 6 red balls.
Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and
variance of the distribution
12
695Two similar boxes ( B_{i}(i=1,2) ) contains ( (i+1) ) red and ( (5-i-1) ) black balls.
One box is chosen at random and two
balls are drawn randomly. What is the probability that both the balls are of
different colours?
A ( cdot frac{1}{2} )
B. ( frac{3}{10} )
( c cdot frac{2}{5} )
D.
12
696The probability of a man hitting a target in one trial is ( frac{1}{4} . ) The chances of hitting the target at least once in ( n ) trials exceeds ( frac{2}{3}, ) then the value of ( n ) equals
( A cdot 2 )
B. 4
( c cdot 6 )
D. 8
12
697A random variable ( boldsymbol{X} ) has the following probability distribution:
[
begin{array}{ccccc}
boldsymbol{X} & 0 & 1 & 2 & 3 \
P(X) & 0.1 & k & 2 k & 2 k
end{array}
]
Determine:
(i) ( k )
(ii) ( P(X geq 2) )
12
698The incidence of occupational disease in an industry is such that the workers have a ( 20 % ) chance of suffering from it. The probability that out of 6 workers chosen at random, not even one will
suffer from that disease is
( mathbf{A} cdotleft(frac{1}{5}right)^{6} )
B. ( left(frac{4}{5}right)^{6} )
( ^{mathbf{c}} cdot_{1}^{6} Cleft(frac{1}{5}right)^{5}left(frac{4}{5}right)^{1} )
( ^{mathrm{D} cdot}_{1}^{6} Cleft(frac{1}{5}right)^{1}left(frac{4}{5}right)^{5} )
12
69910 different pens and two different books are distributed randomly to 3 students giving 4 things to each. The probability that books go to different students is
A ( cdot frac{5}{11} )
в. ( frac{6}{11} )
( c cdot frac{7}{11} )
D. ( frac{8}{11} )
12
7004 bad apples accidentally got mixed up with 20 good apples. In a draw of 2 apples at random, expected number of bad apples is
A . 1
в. ( 2 / 3 )
c. ( 1 / 3 )
D. ( 1 / 6 )
12
701If 3 numbers are selected from the first
15 natural numbers, then the probability that the numbers are in A.P is
A ( cdot frac{7}{65} )
в. ( frac{9}{65} )
( c cdot frac{8}{65} )
D. ( frac{6}{65} )
12
702Which one of the following cannot be the probability of an event
A ( cdot frac{2}{3} )
в. -1.5
c. ( 15 % )
D. 0.7
12
703A box has tokens numbered 3 to 100 . If a
token is taken out at random the
chance that the number is divisible by 7
is
A ( cdot 1 / 4 )
B. 1/5
( c cdot 1 / 6 )
D. 1/
12
704Given ( boldsymbol{X}-boldsymbol{B}(boldsymbol{n}, boldsymbol{p}) )
If ( n=10 ) and ( p=0.4, ) find ( E(X) ) and
( operatorname{Var}(boldsymbol{X}) )
12
705Check whether the probabilities ( boldsymbol{P}(boldsymbol{A}) )
and ( P(B) ) are consistently defined ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
( mathbf{0 . 8} )
12
706Toss three fair coins
simultaneously and record the outcomes. Find the probability of
getting atmost one head in the three tosses.
A ( cdot frac{1}{6} )
B. ( frac{1}{4} )
( c cdot frac{1}{2} )
D.
12
707If ( mathrm{M} ) and ( mathrm{N} ) are any two events, the
probability that not exactly one of them occurs is for an event set ( A ), the
complement is ( boldsymbol{A}^{o} )
A. ( P(M)+P(N)-2 P(M cap N) )
В. ( P(M)+P(N)-P(M cap N) )
C ( cdot Pleft(M^{o}right)+Pleft(N^{o}right)-2 Pleft(M^{o} cup N^{o}right) )
D. ( Pleft(M cap N^{o}right)+Pleft(M^{o} cup Nright) )
12
7081
20. Let X and Y be two events such that P(X) =
(JEE Adv. 2017
and P (Y|X)= -. Then
(a) PCY)=
e) P(KoY)=
(6) P(X”Y)=
(a) P(XUY) =
12
709Given two independence events ( A ) and
( B ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) )
12
710From a lot of 10 bulbs, which includes 3
detectives, a sample of 2 bulbs is drawn at random. Find the probability
distribution of the number of defective
bulbs.
12
71118. Let X and Y be two events such that P(XY)-1
P(Y/X)= ? and P(XnY)= 1. Which of the following is
2. Which of the following is
(are) correct ?
(2012)
(a) P(XUY)=
(b) X and Y are independent
(C) X and Y are not independent
(a) P(xºny) =
12
712If ( mathbf{A} ) and ( mathbf{B} ) are two events such that ( P(mathbf{A} cup B) geq frac{3}{4} ) and ( frac{1}{8} leq P(A cap B) leq frac{3}{8} )
then
This question has multiple correct options
A ( cdot mathrm{P}(mathrm{A})+mathrm{P}(mathrm{B}) leq frac{11}{8} )
в.
c. ( mathrm{P}(mathrm{A})+mathrm{P}(mathrm{B}) geq frac{7}{8} )
D. ( mathrm{P}(mathrm{A}) cdot mathrm{P}(mathrm{B}) geq frac{1}{8} )
12
713Urn ( A ) contains 6 red and 4 black balls
and urn ( B ) contains 4 red and 6 black
balls. One ball is drawn at random from
urn ( A ) and placed in urn ( B ). Then one bal
is drawn at random from urn ( B ) and
placed in urn ( A ). If one ball is now drawn at random from urn ( A ), the probability
that it is found to be red is ( 4 k / 55 . ) Find
the value of ( k )
12
714If the probability of defective bolts is 0.1
the sum of the mean and standard
deviation for the distribution of
defective volts in a total of 500 bolts is ( (a+sqrt{b}), ) then the value of ( a+b ) is
12
715If ( A ) and ( B ) are two events, the
probability that exactly one of them occurs is given by
This question has multiple correct options
A. ( P(A)+P(B)-2 P(A cap B) )
В ( cdot Pleft(A cap B^{prime}right)+Pleft(A^{prime} cap Bright) )
c. ( P(A cap B)-P(A cap B) )
D. ( Pleft(A^{prime}right)+Pleft(B^{prime}right)-2 Pleft(A^{prime} cap B^{prime}right) )
12
716If ( A ) and ( B ) are events of the same
experiments with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})= )
0.5, then find the maximum value of
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
12
717A fair die is rolled once.
STATEMENT – 1: The probability of getting a composite number is ( 1 / 3 )
STATEMENT – 2: There are three
possibilities for the obtained number
( (i) )
the number is a prime number (ii) the number is a composite number (iii) the
number is ( 1, ) and hence probability of
getting a prime number ( =1 / 3 )
A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement – 1
B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement –
c. Statement – 1 is True, Statement – 2 is False
D. Statement – 1 is False, Statement – 2 is True
12
718There are 6 articles in a box. Write the
total numbers of article in 10 such
boxes.
12
719A fair die is thrown 3 times. The chance
that sum of three numbers appearing on the die is less than 11 , is equal to –
A ( cdot frac{1}{2} )
B. ( frac{2}{3} )
( c cdot frac{1}{6} )
D. ( frac{5}{8} )
12
720If ( P(n) ) is the statement ( ” n(n+1) ) is
even”, then what is ( boldsymbol{P}(boldsymbol{4}) ) ?
12
721For two events ( A ) and ( B ), if ( P(A)= ) ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})=mathbf{1} / mathbf{4} ) and ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A})=mathbf{1} / 2, ) then
This question has multiple correct options
A. A and B are independent
B. A and B are mutually exclusive
c. ( Pleft(A^{prime} mid Bright)=3 / 4 )
D. ( Pleft(B^{prime} mid A^{prime}right)=1 / 2 )
12
722Eight players ( boldsymbol{P}_{1}, boldsymbol{P}_{2}, ldots ldots boldsymbol{P}_{8} ) play a
knock-out tournament. It is known that
whenever the players ( P_{i} ) and ( P_{j} ) play,
the player ( boldsymbol{P}_{i} ) will win if ( i<j ). Assuming
that the players are paired at random in each round, the probability that the
player ( boldsymbol{P}_{4} ) reaches the final is ( boldsymbol{k} / mathbf{7} ) 0. Find
( boldsymbol{k} )
12
723Mother, father and son line up at
random for a family photo. If ( A ) and ( B ) are two events given by ( A= ) Son on one
end, ( B= ) Father in the middle, find
( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) )
12
724Let ( A ) and ( B ) be events such that ( boldsymbol{P}(overline{boldsymbol{A}})=frac{4}{5}, boldsymbol{P}(boldsymbol{B})=frac{1}{3}, boldsymbol{P}left(frac{boldsymbol{A}}{boldsymbol{B}}right)=frac{1}{6} )
then:
A ( . P(A cap B) )
в. ( P(A cup B) )
( ^{mathrm{c}} cdot_{P}left(frac{B}{A}right) )
D. Are ( A ) and ( B ) independent
12
725One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a
king?
A ( cdot frac{1}{2} )
в. ( frac{6}{13} )
c. ( frac{7}{13} )
D. ( frac{27}{52} )
12
726For two independent events ( A ) and ( B ) what is ( P(A+B), operatorname{given} P(A)=frac{3}{5} ) and
( P(B)=frac{2}{3} ? )
A ( cdot frac{11}{15} )
в. ( frac{13}{15} )
( c cdot frac{7}{15} )
D. 0.65
12
72713.
At a telephe
a telephone enquiry system the number of phone cells
arding relevant enquiry follow Poisson distribution with
age of 5 phone calls during 10 minute time intervals
be probability that there is at the most one phone call
during a 10-minute time period is
(2006)
(a)
(b)
12
728Three coins are tossed. Find the
probability of getting atleast two head.
12
729A bag contains 10 white and 15 black
balls. Two balls are drawn in succession
without replacement. What is the probability that first is white and second is black?
12
730A person writes letters to six friends
and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that all of them are in wrong envelope.
12
731For any two events ( A ) and ( B ) in a sample
space:
This question has multiple correct options
( ^{mathbf{A}} cdot p(A mid B) geq frac{P(A)+P(B)-1}{P(B)}, P(B) neq 0, ) is always true
B ( . P(A cap bar{B})=P(A)-P(A cap B) ), does not hold
C ( . P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are independent
D ( . P(A cup B)=1-P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint
12
732The odds in favour of India winning any
cricket match is ( 2: 3 . ) What is the
probability that if India plays 5 matches, it wins exactly 3 of them?
( ^{mathbf{A}} cdot_{^{5}} C_{3}left(frac{2}{5}right)^{2}left(frac{3}{5}right)^{3} )
( ^{mathrm{B}} cdot_{^{5}} C_{3}left(frac{2}{3}right)^{2}left(frac{1}{3}right)^{3} )
( ^{mathbf{c}} cdot_{^{5}} C_{3}left(frac{2}{5}right)^{3}left(frac{3}{5}right)^{2} )
( ^{mathrm{D} cdot}^{5} C_{3}left(frac{2}{3}right)^{2}left(frac{1}{3}right)^{2} )
12
733A bouquet from 11 different flowers is to be made so that it contains not less
then three flowers. Then the number of
the different ways of selecting flowers to from the bouquet
A . 1972
в. 1952
c. 1981
D. 1947
12
734Rahim takes out all the hearts from the
cards. What is the probability of

Picking out a card that is not a heart.

12
735Seven digits from the numbers 1,2,3,4 5,6,7,8,9 are written down nonrepeatedly in a random order to form a seven digit number. The probability that this seven digit number is divisible by 9
is
( A cdot frac{2}{9} )
B. ( frac{7}{36} )
( c cdot frac{1}{9} )
( D cdot frac{7}{12} )
12
736A box contains 6 red balls and 2 black
balls. Two balls are drawn at random
from it without replacement. if ( x ) denotes the number of red balls drawn, then find ( boldsymbol{E}(boldsymbol{x}) )
12
737Given that the two numbers appearing on throwing two dice are different.
Find the probability of the event ‘the sum of numbers on the dice is 4
12
738A two digit number is to be formed from the digits ( 0,1,3,4 . ) Repetition of the digits is allowed. Find the probability that number that formed is a –
(1) prime number
(2) multiple of 4
(3) multiple of 11.
12
739Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades
Hence find the mean of the distribution
12
740A coin is tossed 1000 times with the
following frequencies:
Head: ( 445, ) Tail: 555
When a coin is tossed at random, what
is the probability of getting a head?
12
741If ( A ) and ( B ) are independent events such
( operatorname{that} P(A)=0.3 ) and ( P(B)=0.4, ) then find
(i) ( P(A text { and } B) )
(ii) ( P(A text { or } B) )
12
742The chance of throwing a total of 3 or 5
or 11 with two dice is.
A ( cdot frac{5}{36} )
в. ( frac{1}{9} )
( c cdot frac{2}{9} )
D. ( frac{19}{36} )
12
743Assume that the chances of a patient having a heart attack are ( 40 % ). It is also assumed that a meditation and yoga
course reduce the risk of heart attack
by ( 30 % ) and the prescription of certain drugs reduces its chances by ( 25 % ). At a time a patient can choose any one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?
12
744Two dice are thrown. The probability that the sum of the numbers coming up
on them is 9 , if it is known that the
number 5 always occurs on the first die, is
A ( cdot frac{1}{6} )
B. ( frac{1}{3} )
( c cdot frac{1}{2} )
D. ( frac{5}{6} )
12
745A pack of cards was found to contain
only 51 cards. If first 13 cards, which are examined, are all red, then find the probability that the missing cards is black?
A ( cdot 2 / 3 )
в. ( 1 / 3 )
c. ( 2 / 9 )
D. ( 1 / 6 )
12
746The p. ( m ). ( f ). ( X ) -number of major defects randomly selected appliance of a certain type is :
[
x-x
]
( begin{array}{lllll}text { P(a) } & text { 0.08 } & text { 0.15 } & text { 0.45 } & text { 0.27 }end{array} )
Find the expected value and standard deviation of ( X )
12
747If two events ( A ) and ( B ) are such that
( boldsymbol{P}(overline{boldsymbol{A}})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3}, ) then ( boldsymbol{P}left(frac{boldsymbol{B}}{boldsymbol{A} cup overline{boldsymbol{B}}}right) ) is
equal to
A ( cdot frac{5}{8} )
B. ( frac{7}{8} )
( c cdot frac{3}{8} )
D.
12
748A black and a red die are rolled together. Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4
12
749Bag ( A ) contains 2 white and 3 red balls
and bag ( B ) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bag is found to be red. Find the probability that it was drawn from
bag ( boldsymbol{B} )
( A cdot frac{3}{8} )
в. ( frac{25}{52} )
( c cdot frac{1}{8} )
D. ( frac{3}{14} )
12
750A fair coin and an unbiased die are
tossed. Let ( A ) be the event ‘head appears
on the coin’ and ( B ) be the event ‘3 on the
die’. Check whether ( A ) and ( B ) are
independent events or not.
A. True
B. False
12
751Tickets numbered from 1 to 30 are
mixed up and then a ticket is drawn at
random. What is the probability that the
drawn ticket has a number which is
divisible by both 2 and ( 6 ? )
A ( cdot frac{1}{2} )
B. ( frac{2}{5} )
( c cdot frac{8}{15} )
D.
12
752Two events ( A ) and ( B ) are such that
( P(A)=frac{1}{4}, P(B)=frac{1}{2} ) and ( P(B mid A)=frac{1}{2} )
Consider the following statements
( (I) P(bar{A} mid bar{B})=frac{3}{4} )
( (I I) A ) and ( B ) are mutually exclusive
( (I I I) P(bar{A} mid bar{B})+P(A mid bar{B})=1 )
Then
A. Only I is correct
B. Only I and II are correct
c. only ( I ) and ( I I I ) are correct
D. only II and III are correct
12
753A bag contains 4 balls. Two balls are
taken out without replacement and found to be white. Find the probability that all the balls of the bag are white.
12
754You have a spinning wheel with 3 green
sectors, 1 blue sector and 1 red sector, if
the probability of getting a non-blue
sector is ( frac{4}{m} . ) Then, the value of ( m ) is
( A, 5 )
B. 4
( c . )
( D )
12
75529.
A box contains 15 green and 10 yeilow balls. If 10 L
are randomly drawn, one-by-one, with replacement
the variance of the number of green balls drawn is
cement, then
[JEE M 2017
(c) 6
(d) 4
12
756( A, B ) and ( C ) are three mutually
exclusive and exhaustive events such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{2} boldsymbol{P}(boldsymbol{B})=mathbf{3} boldsymbol{P}(boldsymbol{C}) )
What is ( boldsymbol{P}(boldsymbol{B}) ) ?
A ( .6 / 11 )
B. ( 6 / 22 )
c. ( 1 / 6 )
D. ( 1 / 4 )
12
757A committee of two persons is selected from two men and two women. What is
the probability that the committee will
have no man?
12
758Before a race the chances of three
runners, ( A, B, C, ) were estimated to be
proportional to 5,3,( 2 ; ) but during the race ( A ) meets with an accident which
reduces his chance to one-third. What
are now the respective chances of ( boldsymbol{B} )
and ( C ? )
12
759The probability of an ( _{—–} ) is greater
than or equal to 0 and less than or equal
to 1.
A. space
B. experiment
c. sample
D. event
12
760Two dice are thrown. The events
( A, B, C, D, E ) and ( F ) are described as follows:
( A= ) Getting an even number on the
first die.
( B= ) Getting an odd number on the first
die.
( C= ) Getting at most 5 as sum of the number on the two dice.
( D= ) Getting the sum of the numbers on
the dice greater than 5 but less than 10 .
( boldsymbol{E}=operatorname{Getting} ) at least 10 as the sum of the numbers on the dice.
( boldsymbol{F}= ) Getting an odd number on one of
the dice

Describe the following events: ( A ) and ( B, B ) or ( C, B ) and ( C, A ) and ( E, A ) or ( F, A ) and ( boldsymbol{F} )

12
761( A, B, C ) are any three events. If ( P(S) )
denotes the probability of ( S ) happening,
( operatorname{then} boldsymbol{P}(boldsymbol{A} cap(boldsymbol{B} cup boldsymbol{C}))= )
A ( cdot P(A)+P(B)+P(C)-P(A cap B)-P(A cap C) )
B . ( P(A)+P(B)+P(C)-P(B) P(C) )
C ( cdot P(A cap B)+P(A cap C)-P(A cap B cap C) )
D. None of these
12
762Let A and B be two events such that P(AUB)=1
P(AO B)=
and P(A)= =, where A stands for
complement of event A. Then events A and B are
(a) equally likely and mutually exclusive
[2005]
(b) equally likely but not independent
(c) independent but not equally likely
(d) mutually exclusive and independent
12
763Probability of an event is always less than or equal to
A. 0
B. 1
( c cdot> )
D. None of these
12
764Jiah is doing an experiment in her math class. She flips four coins In the air. What is most likely to happen?
A. Two of the coins will be heads and two will be tails
B. Three of the coins will be heads and one will be tail
c. Allfour coins willbe heads
D. None of the coins willbe heads
12
765The probability distribution of a random
variable ( X ) is given below
( boldsymbol{X}=boldsymbol{x} ) ( begin{array}{ll}-1.5 & -0.5end{array} ) ( mathbf{0 . 5} )
( P[X= )
( X] )( quad 0.05 ) 0.25 0.15
The variance of ( boldsymbol{X} ) is
A . 1.6
B. 0.24
c. 0.84
D. 0.75
12
766When the dice are thrown, the event
( E=4, ) then this event is called
A. compound event
B. simple event
c. impossible event
D. complementary event
12
767The probability of a man hitting the ( operatorname{target} ) is ( frac{1}{4} . ) If he fires 7 times, the probability of hitting the target exactly six times is
( ^{mathrm{A}} cdot_{^{7}} C_{5}left(frac{1}{4}right)^{6}left(frac{3}{4}right) )
( ^{mathrm{B} cdot}^{7} C_{6}left(frac{3}{4}right)^{6}left(frac{1}{4}right) )
( ^{mathbf{c}} cdot_{7} C_{6}left(frac{1}{4}right)^{6}left(frac{3}{4}right) )
( ^{mathrm{D} cdot}^{7} C_{6}left(frac{1}{2}right)^{6}left(frac{1}{2}right) )
12
768The PDF of variable x: number of times
sum 6 appears on in two throw of a pair of dice is
[
begin{array}{cc}
mathbf{0} & mathbf{1}
end{array}
]
( p(x) )
then values of ( a, b, c ) are.
A ( cdot a=frac{2}{36}, b=frac{3}{36}, c=frac{5}{36} )
В. ( a=frac{961}{36}, b=frac{310}{36}, c=frac{25}{36} )
( ^{mathbf{C}} cdot_{a}=frac{961}{1269}, b=frac{310}{1296}, c=frac{25}{1296} )
D. ( a=frac{91}{36}, b=frac{30}{36}, c=frac{25}{36} )
12
769If ( boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})=1 ; ) then which of the
following option explains the event ( boldsymbol{A} )
and ( B ) correctly?
A. Event ( A ) and ( B ) are mutually exclusive, exhaustive and complementary events
B. Event ( A ) and ( B ) are mutually exclusive and exhaustive events
C. Event ( A ) and ( B ) are mutually exclusive and complementary events
D. Event ( A ) and ( B ) are exhaustive and complementary events
12
770The probabilities of solving a problem
by three students ( A, B ) and ( C ) are ( frac{1}{2}, frac{3}{4} ) and ( frac{1}{4} ) respectively. The probability that the problem will be solved is
( ^{A} cdot frac{3}{32} )
в. ( frac{3}{16} )
c. ( frac{29}{32} )
D. None of the above
12
771A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is:
A ( cdot frac{2}{13} )
в. ( frac{11}{13} )
c. ( frac{4}{13} )
D. ( frac{8}{13} )
12
772Given two independent events ( A, B )
such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 6} )
Determine
( boldsymbol{P}(boldsymbol{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{n} boldsymbol{o} boldsymbol{B} boldsymbol{B}) )
12
773Suppose values taken by a variable are such that ( a leq x, leq b ) where ( x, ) denote
the value of ( x ) in the ( i^{t h} ) class for ( i= )
( l, 2, cdots n, ) then
A ( cdot a^{2} leq operatorname{Var}(x) leq b )
B cdot ( a^{2} leq a^{2}(x) leq b^{2} )
( ^{mathrm{c}} cdot frac{a^{2}}{4} leq operatorname{Var}(x) )
D. ( operatorname{Var} x leq(b-a)^{2} )
12
774Which of the following is an experiment?
A. Tossing a coin
B. Rolling a single 6 – sided dice
c. choosing a marble from a jar
D. All of the above
12
775There are n different object ( 1,2,3, ldots n )
distributed at random in n boxes
( A_{1}, A_{2}, A_{3}, cdots A_{N} . ) Find the probability
that two objects are placed in the boxes corresponding to their number.
A .
в. ( frac{1}{2} )
( c cdot frac{1}{3} )
D. ( frac{2}{3} )
12
776An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top card is a red card.
12
777Sample space for experiment in which two coins are tossed is
A . 8
B. 4
( c cdot 2 )
D. None of these
12
7787 white balls and 3 black balls are
randomly placed in a row. The probability that no two black balls are placed adjacently equals
A ( cdot frac{1}{2} )
в. ( frac{7}{15} )
c. ( frac{2}{15} )
D.
12
779Two men hit at a target with probabilities ( frac{1}{2} ) and ( frac{1}{3} ) respectively. What is the probability that exactly one of them hits the target?
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{6} )
D. ( frac{2}{3} )
12
780If ( boldsymbol{P}left(boldsymbol{E}_{k}right)=boldsymbol{C} ) for ( mathbf{0} leq boldsymbol{k} leq boldsymbol{n}, ) then the
probability that ( X ) is the only student to pass the examination is
A ( .3 / 4 n )
B. ( 2 /(n+1) )
c. ( 2 / n(n+1) )
D. ( 3 / n(n+1) )
12
781A card is drawn at random from a pack
of 52 cards. Find the probability that the card drawn is a black king.
12
782A bag contains 5 red and 8 white balls. If a ball is drawn at random from the bag,
what is the probability that it will be:
(i) White ball,
(ii) Not a white ball?
12
783If the mean and variance of a binomial
distribution are 4 and 2 respectively,
then the probability of 2 successes of that binomial variate ( boldsymbol{X}, ) is
A ( cdot frac{1}{2} )
в. ( frac{219}{256} )
c. ( frac{37}{256} )
D. ( frac{7}{64} )
12
784Assertion
Let ( A, B ) and ( C ) be three events such
that ( boldsymbol{P}(boldsymbol{C})=mathbf{0} )
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C})=mathbf{0} )
Reason
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B} cup boldsymbol{C})=boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
785A bag contains 3 white, 3 black, and 2 red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red.
A ( cdot frac{1}{4} )
B. ( frac{3}{4} )
( c cdot frac{1}{3} )
D. None of these
12
786A die is thrown, a man ( C ) gets a prize of
Rs. 5 if the die turns up 1 and gets a prize of Rs. 3 if the die turns up ( 2, ) else
he gets nothing, A man ( A ) whose probability of speaking the truth is ( frac{1}{2} )
tells ( C ) that the die has turned up 1 and another man ( B ) whose probability of speaking the truth is ( frac{2}{3} ) tells ( C ) that the
die has turned up 2. Find the
expectation value of ( boldsymbol{C} )
12
787If ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{7}}{mathbf{1 3}}, boldsymbol{P}(boldsymbol{B})=frac{mathbf{9}}{mathbf{1 3}}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
2
– then find ( (mathrm{A} mid mathrm{B}) ) 13
12
788A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
A ( cdot frac{10}{3^{5}} )
в. ( frac{17}{3^{5}} )
c. ( frac{13}{3^{5}} )
D. ( frac{11}{3^{5}} )
12
789-I contains 3 red and 4 black balls Bag
while another Bag -ll contains 5 red and 6 black b alls. One ball is drawn at
random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag -II.
12
790For the probability distribution function
of random variable ( X, x_{1}, x_{2}, x_{3}, dots x_{n} )
are the values ( X ) takes, and ( pleft(x_{i}right) )
denote the probability of ( x_{i} ) then which
one of the following is true.? This question has multiple correct options
( mathbf{A} cdot pleft(x_{i}right)>0 )
в. ( pleft(x_{i}right)<0 )
( mathbf{c} cdot sum pleft(x_{i}right)=1 )
D. ( sum x_{i}=1 )
12
791In a survey of 500 ladies, it was found that 180 like coffee
while rest of the ladies dislike it. From these ladies, one is
chosen at random. What is the probability that the chosen
lady dislikes coffee?
11
792One hundred identical coins, each with
probability ( p, ) of showing up heads are tossed. If ( 0<p<1 ) and the probability
of heads showing on 50 coins is equal to that of the heads showing in 51 coins, then the value of ( p ) is
A ( cdot frac{1}{2} )
в. ( frac{49}{101} )
c. ( frac{50}{101} )
D. ( frac{51}{101} )
12
793If ( phi ) represents an impossible event then ( boldsymbol{P}(phi)=? )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot phi )
D. –
12
794Two dice are thrown:
( P ) is the event that the sum of the
scores on the uppermost faces is a
multiple of 6
( Q ) is the event that the sum of the
scores on the uppermost faces is at
least 10
( R ) is the event that same scores on both
dice.

Which of the following pairs is mutually exclusive?
A. ( P, Q )
в. ( P, R )
( mathbf{c} cdot Q, R )
D. None of these

12
795( A ) and ( B ) are two independent events.
The probability that both ( A ) and ( B ) occur is ( 1 / 6 ) and the probability that at least
one of them occurs is ( frac{2}{3} . ) The probability of the occurrence of ( boldsymbol{A}=ldots ldots ldots ) if ( boldsymbol{P}(boldsymbol{A})= )
( 2 P(B) )
( A cdot frac{2}{9} )
в. 4
( c cdot frac{5}{9} )
D. ( frac{5}{18} )
12
796Five ordinary dies are rolled at random and the sum of numbers shown is 16
What is the probability that the number
shown on each is any one from 2,3,4 or
( mathbf{5} ? )
A ( cdot frac{9}{49} )
B. ( frac{3}{49} )
c. ( frac{2}{49} )
D. None of these
12
797100 tickets are numbered as 00,01,02
( ldots .09,10,11,12, ldots .99 . ) Out of them, one
ticket is drawn at random. The
probability that the sum of the digits of the number on the ticket is 9 is
A. ( frac{7}{100} )
в. ( frac{9}{100} )
c. ( frac{1}{10} )
D. ( frac{1}{100} )
12
798Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( P(A / B) )
12
799If ( mathrm{E} & mathrm{F} ) are events with ( boldsymbol{P}(boldsymbol{E}) leq boldsymbol{P}(boldsymbol{F}) & )
( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})>0, ) then
A. occurrence of ( E Rightarrow ) occurrence of ( F )
B. occurrence of FRightarrow occurrence of E
c. non occurrence of ( E Rightarrow ) non occurrence of ( F )
D. none of the above implications holds
12
800A bag contains 8 red, 6 white and 4
black balls. A ball is drawn at random
from the bag. Find the probability that the drawn ball is
(i) red or white
(ii) not black
neither white nor black
12
8013.
A dice is tossed 5 times. Getting an odd numbe
a success. Then the variance of distribution o
(2) 8/3 (6) 318 (c) 4/5 (d) 5/4
The mean and
blo y having
Jetting an odd number is considered
Then the variance of distribution of success is 2002
12
802The probability that Chakri passes in mathematics is ( frac{2}{3} ) and the probability that he passes in English is ( frac{4}{9} . ) If the probability of passing both courses is ( frac{1}{4}, ) then the probability that Chakri wil pass in at least one of these subjects is ( mathbf{3 1} )
立 ( overline{mathbf{3 6}} )
A . True
B. False
c. Ambiguous
D. Data Insufficient
12
803If ( A ) and ( B ) are two events in a sample
space ( S ) such that ( P(A) neq 0, ) then
( Pleft(frac{B}{A}right)= )
A ( cdot P(A) cdot P(B) )
в. ( frac{P(A cap B)}{P(B)} )
c. ( frac{P(A cap B)}{P(A)} )
D ( cdot P(B) )
12
804A balloon vendor has 2 red,3 blue and 4
green balloons. He wants to choose one
of them at random to give it to Pranali. What is the probability of the event that Pranali gets:
(i) a red balloon
(ii) a blue balloon
(iii) a green balloon.
12
805A man is know to speak the truth 3 out if 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is:
A ( cdot frac{3}{8} )
B. ( frac{1}{5} )
( c cdot frac{3}{4} )
D. None of these
12
806In a single throw of a die, the events {1,2},{2,3} are mutually exclusive. Write 1 if true and 0 if false.12
807If ( A ) and ( B ) are two events such that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6 5} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= )
( mathbf{0 . 1 5}, operatorname{then} boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= )
A . 0.6
B. 0.8
c. 1.2
D. 1.
12
808The probabilities of ( x, y ) and ( z ) becoming manager are ( frac{4}{9}, frac{2}{9} & frac{1}{3} ) respectively. The probabilities that the bonus scheme will be introduced if ( x, y ) and ( z ) become managers are ( frac{3}{10}, frac{1}{2} & frac{2}{5} ) respectively. Find
(i) What is the probatility that the bonus scheme will be introduced? (ii) if
the bonus scheme has teen introduced,
What is the probability that the manager appointed wax ( x ? )
12
809If for a binomial distribution ( bar{x}=frac{6}{5} ) and the difference between mean and variance is ( frac{6}{25} . ) The number of trials is
A . 8
B. 7
( c .6 )
D.
12
810If ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{3}}{boldsymbol{4}}, boldsymbol{P}left(boldsymbol{B}^{prime}right)=frac{1}{3} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{P}(boldsymbol{A} cap )
( B)=frac{1}{2} ) then find ( P(A cup B) )
A ( cdot frac{5}{12} )
в. ( frac{6}{12} )
c. ( frac{7}{12} )
D. ( frac{11}{12} )
12
811A pair of number cubes is rolled up.What is the probability that the sum is odd given that the sum is greater than or equal to 9
A ( cdot frac{1}{6} )
в. ( frac{3}{28} )
( c cdot frac{2}{6} )
D.
12
812The probability of picking a number which ends with 3 from first 100 natural
numbers is
A . ( 0 . )
B. 0.3
c. 0.13
D. none
12
813A coin is tossed. Find the total number
of elementary events and also the total number events associated with the
random experiment.
12
814Two unbiased dice are rolled once. Find
the probability of getting a doublet.
A ( cdot frac{1}{6} )
B. ( frac{3}{4} )
( c cdot frac{2}{3} )
D.
12
8157.
When a die is thrown, list the outcomes of an event of
getting
(1) (a) a prime number (b) not a prime number.
(ii) (a) a number greater than 5
(b) a number not greater than 5.
11
816A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?
A ( cdot frac{2}{9} )
в. ( frac{1}{14} )
c. ( frac{2}{63} )
D. ( frac{2}{14} )
12
817One of the two boxes, box ( boldsymbol{I} ) and box ( boldsymbol{I} boldsymbol{I} )
was selected at random and balls are
drawn randomly out of this box. The ball was found to be red.If the probability
that this red ball was drawn from box ( I I )
is ( frac{1}{3}, ) then the correct option options
with the possible values of ( n_{1}, n_{2}, n_{3} )
and ( n_{4} ) is (are)
This question has multiple correct options
( mathbf{A} cdot n_{1}=3, n_{2}=3, n_{3}=5, n_{4}=15 )
B . ( n_{1}=3, n_{2}=6, n_{3}=10, n_{4}=50 )
C ( . n_{1}=8, n_{2}=6, n_{3}=5, n_{4}=20 )
D ( cdot n_{1}=6, n_{2}=12, n_{3}=5, n_{4}=20 )
12
8182.
Assertion: Weighing of an apple is an example of random
experiment.
Reason: A random experiment is that in which outcomes
may differ each time when we perform an experiment.
11
819If each element of a second order
determinant is either zero or one, what
is the probability that the value of the determinant is positive? (Assume that the individual entries of the
determinant are chosen independently,
each value being assumed with probability ( left.frac{1}{2}right) )
12
820In a class of 50 boys, 35 like horror movies, 30 like war movies and 5 like neither. Find the number of those that
like both.
A . 20
B . 25
c. 15
D. 28
12
821Assertion
If the independent events ( boldsymbol{A} & boldsymbol{B} ) are
such that ( mathbf{0}<boldsymbol{P}(boldsymbol{A})<mathbf{1}, mathbf{0}<boldsymbol{P}(boldsymbol{B})< )
1, then ( A & B ) can not be mutually
exclusive.
Reason
Two events ( A & B ) can not be mutually
exclusive, if ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) neq mathbf{0} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
822Ta
U
1 ) (u 8/9.
given that the events A and B are such that
16.
It is given that
P(A) = 1, PCAB) = and PCB | 4) = . Then P(B) is
[2008]
is thrown Let A be the event that the number obtain
12
823( A ) and ( B ) are two events where ( P(A)= ) 0.25 and ( P(B)=0.5 . ) The probability of
both happening together is 0.14 . The
probability of both ( A ) and ( B ) not happening is
A . 0.39
B. 0.25
c. 0.11
D. none of these
12
824A fair die is rolled. Find the probability
of getting the number 5
A ( cdot frac{1}{6} )
в. ( frac{5}{6} )
( c cdot frac{2}{6} )
D. ( frac{3}{6} )
12
825If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) . boldsymbol{A} ) and ( boldsymbol{B} ) are two
non-mutually exclusive events then
A. ( A ) and ( B ) are necessarily same events
в. ( P(A)=P(B) )
c. ( P(A cap B)=P(A) P(B) )
D. all the above
12
826Three fair coins are tossed
simultaneously. If X denotes the number of heads, find the probability distribution of ( X )
12
827The mode of the binomial distribution
for which mean and standard deviation
are 10 and ( sqrt{5} ) respectively, is
A. 7
B. 8
( c .9 )
D. 10
12
828The probability of an event is
A. always more than 1
B. always less than 1
c. always equal to
D. always negative
12
829Three fair dice are thrown. The
probability of getting a sum 6 or less on the three dice is
( ^{A} cdot frac{7}{12} )
в. ( frac{5}{54} )
c. ( frac{19}{216} )
D. ( frac{11}{108} )
12
830Let ( A ) and ( B ) be two independent events.
The probability that both ( A ) and ( B ) happen is ( frac{1}{12} ) and the probability that neither ( A ) nor ( B ) happen is ( 1 / 2 ).If the sum of probabilities of occurence of ( boldsymbol{A} ) and ( B ) is ( frac{k}{12}, ) then the value of ( k ) is
12
831( A ) and ( B ) are seeking admission into
IIT. If the probability for ( A ) to be
selected is 0.5 and that both to be
selected is ( 0.3, ) them is it possible that,
the probability of ( B ) to be selected is 0.9
( ? )
12
832Two persons ( A ) and ( B ) are throwing an unbiased six faced die alternatively, with the condition
that the person who throws 3 first wins
the game. If A starts the game, the
probabilities of ( A ) and ( B ) to win the same are
respectively
A ( cdot frac{6}{11}, frac{5}{11} )
B . ( frac{5}{11}, frac{6}{11} )
c. ( frac{8}{11}, frac{3}{11} )
D. ( frac{3}{11}, frac{8}{11} )
12
833An urn contains 4 red and 7 blue balls.
Find the probability of getting Blue balls
12
834A quadratic equation ( a x^{2}+b x+c=0 )
with distinct coefficients is formed. It a
b, c are chosen from the numbers 2,3,5 then the probability that the equation has real roots is
A ( cdot frac{1}{3} )
B. ( frac{2}{5} )
( c cdot frac{1}{4} )
D.
E ( cdot frac{2}{3} )
12
835Two coins are tossed once. Find the
probability of getting:
(i) 2 heads
(ii) at least 1 tail
12
836The length of similar components
produced by a company is approximated by a normal distribution model with a mean of ( 5 mathrm{cm} ) and a
standard deviation of ( 0.02 mathrm{cm} . ) If a
component is chosen at random.what
is the probability that the length of this component is between 4.98 and 5.02
( mathrm{cm} ? )
( mathbf{A} cdot 0.5826 )
B . 0.6826
c. 0.6259
D. 0.6598
12
8374.
Getting a number less than 1 when a die is thrown.
10
838The events ( E_{1}, E_{2}, ldots ldots . . ) represents the
partition of the sample space ( S ), if they
are:
A. pairwise disjoint
B. exhaustive
c. have non-zero probabilities
D. All are correct
12
839From a standard deck of cards, one card is drawn. Find the probability that the card is red and a queen
A ( cdot frac{1}{2} )
в. ( frac{4}{13} )
c. ( frac{1}{26} )
D. ( frac{12}{13} )
12
840A factory has three machines ( A, B ) and ( C ) which produce 100,200 and 300 items of a particular type daily. The machines produce ( 2 %, 3 % ) and ( 5 % ) defective items respectively. One day when the production was over, an item was picked up randomly and it was found to be defective. Find the probability that it was produced by machine ( A )12
841Probability of impossible event is
( A cdot 1 )
B. 0
( c cdot frac{1}{2} )
D. –
12
842A number is selected from the set ( {1,2, ) 3,4,5,6,7,8}( . ) What is the probability that it will be the root of the equation
( x^{2}-6 x+8=0 ? )
12
843Assume that the chances of a patient
having a heart attack is ( 40 % ). Assuming that a mediation and yoga course
reduces the risk of heart attack by ( 30 % ) and prescription of certain drug reduces its chance by ( 25 % ). At a time a patient can choose any one of the two options with equal possibilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of mediation and yoga. Interpret the result and state which of the above
stated methods is more beneficial for
the patient.
12
844If
( A, B ) and ( C ) are three events such that ( P(B)=frac{3}{4}, Pleft(A cap B cap C^{prime}right)=frac{1}{3} ) and
( Pleft(A^{prime} cap B cap C^{prime}right)=frac{1}{3}, operatorname{then} P(B cap C) ) is
equal to
A ( cdot frac{1}{12} )
B.
c. ( frac{1}{15} )
D.
12
845There are 30 tickets in a box numbered
from 1 to ( 30 . ) A ticket is drawn out at
random. Let ( A ) be the event that the
number on the ticket is a multiple of 6
Write the sample set ( S ) and outcomes of
event ( A ) in set form.
12
846A bag contains 6 balls. Two balls are
drawn and found to be red. The
probability that five balls in the bag are red
A ( cdot frac{5}{6} )
в. ( frac{12}{17} )
( c cdot frac{1}{3} )
D.
12
847If ( A ) and ( B ) are events such that
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap )
( boldsymbol{B})=mathbf{0 . 2}, ) find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) and ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) )
12
848A coin is tossed ( 2 n ) times. The chance
that the number of times one gets head is not equal to the number of times one
gets tail is
A ( cdot frac{(2 n) !}{(n ! !)^{2}} cdotleft(frac{1}{2}right)^{2} n )
B. ( _{1-} frac{(2 n) !}{(n !)^{2}} )
c. ( _{1-} frac{(2 n) !}{(n !)^{2}} cdot frac{1}{4^{n}} )
D. none of these
12
849A coin is tossed three times. Find
( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ) in given cases:
( A=A t ) most two tails, ( B=A t ) least one
tail.
12
850Two events ( A ) and ( B ) will be
independent, if
( mathbf{A} . A ) and ( B ) are mutually exclusive
B ( cdot Pleft(A^{prime} B^{prime}right)=[1-P(A)][1-P(B)] )
( mathbf{c} cdot P(A)=P(B) )
D ( cdot P(A)+P(B)=1 )
12
851Five dice are thrown simultaneously. If
the occurrence of an odd number in a
single dice is considered a success, find the probability of maximum three
successes.
12
852The probability distribution function of a random variable ( boldsymbol{X} ) is given by
( boldsymbol{x}_{i}: quad 0 quad 1 quad 2 )
[
begin{array}{lll}
3 c & 4 c & c-1
end{array}
]
where ( c>0 . ) Find ( c )
12
853To know the opinion of the student about the subject statistic, a survey of
200 students was conducted.
The data is recorded in the following table
opinion 1 Like Dislike
No. of Students 65 135
Find the probability that a student chosen at random
( (i) ) likes statistics,
( (i i) ) does not like it.
A.
[
begin{array}{l}
(i) frac{13}{40} \
(i i) frac{19}{40}
end{array}
]
в.
[
(i) frac{27}{40}
]
( (i i) frac{13}{40} )
c.
[
(i) frac{17}{40}
]
( (i i) frac{29}{40} )
D. None of these
12
854( 2 n ) boys are randomly divided into two
subgroups containing ( n ) boys each. The
probability that the two tallest boys are in different groups is
A ( . n /(2 n-1) )
B. ( (n-1) /(2 n-1) )
c. ( (n-1) / 4 n^{2} )
D. None of these
12
855What is the probability of an event?11
856Three candidates solve a question. Odds
in favour of the correct answer are 5 :
2,4: 3 and 3: 4 respectively for the three candidates. What is the
probability that at least two of them solve the question correctly?
A ( cdot frac{209}{343} )
в. ( frac{134}{343} )
c. ( frac{149}{343} )
D. ( frac{60}{343} )
12
857By examine the chest the chest ( X- ) ray probability that ( T . B ) is detected when a
person is actually suffering is ( 0.99 . ) The probability that the doctor diagnoses incorrectly that a person has ( T . B ) on the bases of ( X- ) ray is ( 0.001 . ) In a certain city 1 in 1000 person suffers from ( T . B ) A person is selected at random is
diagnoses to have ( T . B ). What is the
chance that the actually has ( T . B ? )
12
858A die is thrown twice and the sum of the
numbers appearing is observed to be 7 Find the conditional probability that the
number 3 has appeared at least once.
12
859State which of the following are not the
probability distributions of a random
variable. Give reasons for your answer.
( (i) )
begin{tabular}{|c|l|l|l|}
hline ( mathrm{X} ) & 0 & 1 & 2 \
hline ( mathrm{P}(mathrm{X}) ) & 0.4 & 0.4 & 0.2 \
hline
end{tabular}
(ii) begin{tabular}{|c|l|l|l|c|l|}
hline ( mathrm{X} ) & 0 & 1 & 2 & 3 & 4 \
hline ( mathrm{P}(mathrm{X}) ) & 0.1 & 0.5 & 0.2 & -0.1 & 0.3 \
hline
end{tabular}
(iii) begin{tabular}{|c|r|l|l|}
hline ( mathrm{Y} ) & -1 & 0 & 1 \
hline ( mathrm{P}(mathrm{Y}) ) & 0.6 & 0.1 & 0.2 \
hline
end{tabular}
(iv) begin{tabular}{|c|l|l|l|l|l|}
hline ( mathrm{Z} ) & 3 & 2 & 1 & 0 & -1 \
hline ( mathrm{P}(mathrm{Z}) ) & 0.3 & 0.2 & 0.4 & 0.1 & 0.05 \
hline
end{tabular}
12
860A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while ( mathrm{Mr} ) Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is:
A ( cdot frac{1}{18} )
в. ( frac{1}{9} )
( c cdot frac{1}{6} )
D. None of these
12
861If two events ( A ) and ( B ) are such that
( P(bar{A})=frac{3}{10}, P(B)=frac{2}{5} ) and ( P(A cap )
( bar{B})=frac{1}{2}, operatorname{then} Pleft(frac{B}{A cup bar{B}}right) ) is
A ( cdot frac{1}{2} )
B.
( c cdot frac{1}{4} )
D.
12
862A lot contains 20 articles. The
probability that the lot contains exactly
2 defective articles is ( 0 cdot 4 ) and that lot
contains exactly 3 defective articles is
( 0 cdot 6 . ) Articles are drawn from the lot at
random one by one without replacement and are tested till all defective articles
are found. The probability that testing procedure ends at the twelfth testing is
( frac{11 k}{1900} . ) Find the value of ( k ? )
12
863If ( A & B ) are independent events such ( operatorname{that} P(B)=frac{2}{7}, P(A cup bar{B})=0.8, ) then
( P(A) ) is equal to
A . ( 0 . )
B. 0.2
( c .0 .3 )
D. 0.4
12
864The mean and variance of Binomial
Distribution are 4 and 2 respectively, then the probability of success is
A ( cdot frac{128}{256} )
в. ( frac{219}{256} )
c. ( frac{37}{256} )
D. ( frac{28}{256} )
12
865A fair die is rolled. Consider events ( boldsymbol{E}= )
( {1,3,5}, F={2,3} ) and ( G= )
{2,3,4,5} Find
(i) ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) ) and ( boldsymbol{P}(boldsymbol{F} mid boldsymbol{E}) )
(ii) ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{G}) ) and ( boldsymbol{P}(boldsymbol{G} mid boldsymbol{E}) )
(iii) ( P((E cup F) mid G) ) and ( P((E cap F) mid G) )
12
866For a binomial distribution if ( boldsymbol{P}=frac{mathbf{2}}{mathbf{3}} )
and ( n=10 ) the probability of mode is
( ^{mathbf{A}} cdot_{^{10}} C_{4}left(frac{1}{3}right)^{7}left(frac{2}{3}right)^{3} )
( ^{mathrm{B}} cdot_{^{10}} C_{7}left(frac{2}{3}right)^{7}left(frac{1}{3}right)^{3} )
( ^{c}left(frac{2}{3}right)^{7}left(frac{1}{3}right)^{3} )
( ^{text {D }}left(frac{1}{3}right)^{7}left(frac{2}{3}right)^{3} )
12
867For three events ( A, B ) and ( C, P ) (exactly one of the events ( A text { occur })=P ) (exactly
one of the events ( B text { and } C text { occur })=P ) (exactly one of the events ( C ) or ( A ) occurs) ( =mathrm{p} ) and ( mathrm{P} ) (all the three events occur
simultaneously) ( =p^{2}, ) where ( 0<p< )
1/2. If the probability of at least one of
the three events ( A, B ) and ( C ) occurs is
( 11 / 18, ) the value of ( p ) is
A ( cdot 1 / 6 )
в. ( 1 / 4 )
c. ( 1 / 5 )
D. ( 1 / 3 )
12
868A box contains 2 silver coins and 4 gold coins and the second box contains 4
silver coins and 3 gold coins. If a coin is
selected from one of the box, what is the
probability that it is a silver coin.
A . 0.3
B. 0.4
c. 0.5
D. 0.6
12
869Assertion
( boldsymbol{P}(boldsymbol{H} / boldsymbol{E})>boldsymbol{P}left(boldsymbol{E} / boldsymbol{H}_{i}right) boldsymbol{P}left(boldsymbol{H}_{i}right), boldsymbol{i}= )
( mathbf{1}, mathbf{2}, mathbf{3}, dots, boldsymbol{n} . operatorname{Let} boldsymbol{H}_{1}, boldsymbol{H}_{2}, boldsymbol{H}_{3}, dots . . boldsymbol{H}_{n} ) be ( mathbf{n} )
mutually exclusive & exhaustive
events with probability ( boldsymbol{P}left(boldsymbol{H}_{boldsymbol{i}}right)>mathbf{0}, boldsymbol{i}= )
( 1,2,3, dots n . ) Let ( E ) be any other event with
( mathbf{0}<boldsymbol{P}(boldsymbol{E})<mathbf{1} )
Reason
( sum_{i=1}^{n} boldsymbol{P}left(boldsymbol{H}_{i}right)=mathbf{1} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
870Assertion
For any two events ( A ) and ( B ) ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B})=boldsymbol{P}(boldsymbol{B})-boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
Reason
( A cap B ) and ( bar{A} cap B ) are mutually
exclusive events.
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
871Three unbaised coins are tossed find
the probability distribution of the
number of heads occurring on the
topmost faces.
12
872Find the mean number of heads in three
tosses of a fair coin.
12
873The conditional probability that ( X geq 6 )
given the ( X>3 ) equals
A ( cdot frac{125}{216} )
в. ( frac{25}{216} )
c. ( frac{5}{36} )
D. ( frac{25}{36} )
12
874If the variance of the random variable ( boldsymbol{X} )
is ( 5, ) then the variance of the random
variable ( -mathbf{3} boldsymbol{X} ) is
A . 15
B . 45
c. -45
D. 60
12
875One Indian and four American men and
their wives are to be seated randomly around a circular table. Then the
conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is
A . ( 1 / 2 )
B. ( 1 / 3 )
( c cdot 2 / 5 )
D. ( 1 / 5 )
12
876A bag contains some white and some
black balls, all of which are
distinguishable from each other, all combinations of balls being equally likely. The total number of balls in the
bag is ( 10 . ) If three balls are drawn at random and all of them are found to be
black, the probability that the bag contains 1 white and 9 black balls is :
A ( cdot frac{14}{55} )
B. ( frac{12}{55} )
c. ( frac{8}{55} )
D. ( frac{2}{11} )
12
877In 15 throws of a die 4 or 5 is considered
to be a success. The mean number of
success is
A . 3
B. 4
( c .5 )
D. 6
12
878There are 4 horizontal and 6 vertical
equispaced lines as shown.lf a
rectangle is randomly selected then
probability that is a square is
( ^{A} cdot frac{7}{45} )
в. ( frac{13}{45} )
c. ( frac{11}{18} )
( D )
12
879A lot consists of 144 ball pens of which
20 are defective and others are good.
Nuri will buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the
probability that
(i) She will buy it
(ii) She will not buy it
12
880A school has five houses ( A, B, C, D ) and ( E )
A class has 23 students, 4 from house
A, 8. from house B, 5 from house C, 2
from house 0 and rest from house ( mathrm{E} )
A single student is selected at random ,to be the class monitor. The probability that the selected student is not from ( A ),
Band C is?
( mathbf{A} cdot frac{4}{23} )
B. ( frac{6}{23} )
( c cdot frac{8}{23} )
D. ( frac{17}{23} )
12
881There are 7 defective items in a sample
of 35 items. Find the probability that an item chosen at random is non-defective.
12
882A bag contains 8 red and 5 white balls.
Two successive draws of 3 balls are
made at random from the bag without replacements. Find the probability that the first draw yields 3 white balls and the second draw 3 red balls.
12
883If ( A ) and ( B ) are arbitrary events, then
( mathbf{A} cdot P(A cap B) geq P(A)+P(B) )
B ( cdot P(A cap B) leq P(A)+P(B) )
C ( cdot P(A cap B)=P(A)+P(B) )
D. none of these
12
884Consider the experiment of throwing a die, if a multiple of 3 comes up, throw
the die again and if any other number comes, toss a coin. Find the conditional
probability of the event ‘the coin shows a tail’, given that ‘at least one die shows
a 3 ‘.
12
885When a coin is tossed at random, then
the probability of getting a head is
A . 0
B. ( frac{1}{2} )
( c .1 )
D. 2
12
88615 coupons are numbered ( 1,2,3, dots, 15 )
respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
( ^{A} cdotleft(frac{9}{16}right)^{6} )
( ^{mathrm{B}}left(frac{8}{15}right)^{7} )
( ^{c}left(frac{3}{5}right)^{7} )
D. ( frac{9^{7}-8^{7}}{15^{7}} )
12
887Suppose ( X ) has a binomial distribution with ( n=6 ) and ( p=frac{1}{2} . ) Show that ( X=3 )
is the most likely outcome.
12
888Let ( A ) and ( B ) be two events such that
( P(overline{A cup B})=frac{1}{6}, P(A cap B)=frac{1}{4} ) and
( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for the
complement of the event A. Then the
events ( A ) and ( B ) are?
A. Independent but not equally likely
B. Independent and equally likely
c. Mutually exclusive and independent
D. Equally likely but not independent
12
889If ( A, B ) are two events with
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 5} )
then find the value of ( boldsymbol{P}left(boldsymbol{A}^{c}right)+boldsymbol{P}left(boldsymbol{B}^{c}right) )
12
890If atleast one child in a family with 3 children is a boy then the probability that 2 of the children are boys, is
( A cdot frac{3}{7} )
B. ( frac{4}{7} )
( c cdot frac{1}{3} )
D. ( frac{3}{8} )
12
89110.
If E and F are the complementary events of events E and
Frespectively and if 0 <P(F)< 1, then (1998 – 2 Marks)
(a) P(E/F) + P(E / F)=1
(b) P(E/F) + P(EIF)=1
(c) P(Ē / F) + P(E/F)=1
(d) P(EIF)+P(EIF)=1
12
892Nayan tosses a coin thrice. Find the
probability of getting a) exactly 2 heads
and
b) at most 2 tails
12
893Out of 800 families with 4 children
each, the expected number of families
having 2 boys and 2 girls
A. 100
в. 200
c. 300
D. 400
12
894The probability that ( boldsymbol{P} cap boldsymbol{Q}=boldsymbol{A} )
contains just one element, is
( ^{mathrm{A}} cdot_{n}left(frac{3}{4}right)^{n} )
B. ( left(frac{1}{4}right)^{n} )
c. ( frac{n}{3}left(frac{1}{2}right)^{n} )
D. ( left(frac{3}{4}right)^{n} )
12
895How many play cricket only?12
896A pair of dice is thrown 4 times. If
getting a total of 9 in a single throw is considered as a success then find the
mean and variance of successes.
12
897A bag ( A ) contains 10 white and 3 black
balls. Another bag ( B ) contains 3 white
and 5 black balls. Two balls are
transferred from bag ( A ) and put in the bag ( B ) and a ball is drawn from bag ( B )
Find the probability that the ball drawn is white ball.
12
898f ( n(A)=18, n(B)=12, ) and ( A cap B= )
( emptyset, operatorname{then} n(A cup B)= )
( A cdot 6 )
B. 12
( c .30 )
D. 20
12
899Two different families ( A ) and ( B ) are
blessed with equal number of children.
There are 3 tickets to be distributed
amongst the children of these families so that no child gets more than one
ticket. If the probability that all the tickets go to the children of the family ( B ) is ( frac{1}{12}, ) then the number of children in
each family is?
A .4
B. 6
( c .3 )
( D )
12
900Probability that ( A ) speaks truth is ( frac{4}{5} . A ) coin is tossed. A reports that a head appears. The probability that actually there was head is
A ( cdot frac{4}{5} )
B. ( frac{1}{2} )
c. ( frac{1}{5} )
D. ( frac{2}{5} )
12
901In a school, ( frac{5}{8} ) of the total students are girls. If the number of girls is 120 more than that of the boys. What is the strength of the school? how many boys are there?
A .160
в. 120
c. 100
D. 180
12
902How many coins are to be tossed at
once to get 64 outcomes in total?
12
903In a hostel, ( 60 % ) of the students read Hindi news paper, ( 40 % ) read English
news paper and ( 20 % ) read both Hindi
and English news papers. A student is selected at random.
(a) Find the probability that she reads neither Hindi nor English news papers.
(b) If she reads Hindi news paper, find the probability that she reads English
news paper
(c) If she reads English news paper, find the probability that she reads Hindi
news paper.
A ( .0 .56,0.78,0.76 )
в. 0.20,0.33,0.50
( c .0 .65,0.45,0.34 )
D. 0.56,0.56,0.65
12
904Shekar is one member of a group of 5
persons. If 3 out of these 5 persons is to be chosen for a committee, find the probability of Shekar being in the committee
12
905The probability that a number selected at random from the numbers
( mathbf{1}, mathbf{2}, mathbf{3} dots dots mathbf{1 5} ) is a multiple of ( mathbf{4} ) is
A ( cdot frac{4}{15} )
в. ( frac{2}{15} )
c. ( frac{1}{15} )
D.
12
906If the variance of the random variable ( boldsymbol{X} )
is ( 4, ) then the variance of the random
variable ( 5 X+10 ) is
A. 100
B. 10
c. 50
D. 25
12
907STATEMENT – 1: Dependent events are those in which the outcome of one does not affect and is not affected by the
other.
STATEMENT – 2 : Dependent events are
those in which the outcome of one
affects and is affected by the other.
A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement- –
B. Statement-1 is True, Statement- 2 is True: Statement 2 is NOT a correct explanation for Statement-
c. statement- 1 is True, Statement – 2 is False
D. Statement – 1 is False, Statement- 2 is True
12
908A man take a step forward with
probability 0.4 and backward with probability ( 0.6 . ) The probability that at the end of eleven steps he is one step away from the starting point, is
A . 0.37
в. 0.57
c. 0.3
D. None of these
12
909The number of ways in which 6 men can be arranged in a row, so that three particular men are consecutive, is
A ( .4 ! times 3 ! )
в. ( 4 ! )
c. ( 3 ! times 3 ! )
D. none of these
12
910If ( A ) and ( B ) are two event such that
( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then
( ^{mathbf{A}} cdot P(A cup B) geq frac{3}{4} )
В. ( P(bar{A} cap B) leq frac{1}{4} )
c. ( frac{3}{8} leq P(A cap B) leq frac{5}{8} )
D. All of these
12
911A number consists of 7 digits whose
sum is ( 59 ; ) prove that the chance of its being divisible by 11 is ( frac{4}{21} )
12
912If ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{boldsymbol{4}}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} ) and
( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B} cap overline{boldsymbol{C}})=frac{1}{3} operatorname{then} boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is
A ( cdot frac{1}{12} )
B.
c. ( frac{1}{15} )
( D )
12
913A card is drawn at random from a well
shuffled pack of 52 cards. The probability that the cards drawn is
neither a red card nor a queen is
A ( cdot frac{6}{13} )
в. ( frac{5}{13} )
c. ( frac{4}{13} )
D. ( frac{2}{13} )
12
914Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is less than 14
A ( cdot frac{3}{27} )
в. ( frac{3}{29} )
( c cdot frac{3}{25} )
D. ( frac{3}{22} )
12
915A committee of 4 students is selected
at random from a group consisting of 8 boys and 4 girls. Given that there is at least one girl in the committee, the
probability that there are exactly 2 girls in the committee is
A ( cdot frac{168}{4558} )
B. ( frac{85}{99} )
( mathbf{c} cdot frac{_{5}}{165} )
D. ( frac{14}{999} )
12
916A bag contains 4 identical red balls and
3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?
12
917The G.M of the numbers ( 3^{1}, 3^{2}, 3^{3}, ldots, 3^{3 n} ) is
A ( cdot frac{n}{2} )
в. ( frac{3 n}{2} )
c. ( frac{3 n+1}{2} )
D. ( frac{n+1}{2} )
12
918Which of the following is an outcome?
A. Rolling a pair of dice
B. Landing on red
c. choosing 2 marbles from a jar
D. None of the above
12
919The probability that a student will pass
the final examination in both English and Hindi is 0.5 and the probability of passing neither is ( 0.1 . ) If the probability of passing the English examination is 0.75 What is the probability of passing the Hindi examination
12
920In a survey conducted among 400 students of ( X ) standard in Pune district,
187 students offered to join Science faculty after ( X ) standard and 125
students offered to join Commerce
faculty after ( X ). If a student is selected
at random from this group, find the probability that the student prefers Science or Commerce faculty.
12
921At a certain university, ( 4 % ) of men are
over 6 feet tall and ( 1 % ) of women are over
6 feet tall. The total student population
is divided in the ratio 3: 2 in favour of
women. If a student is selected at
random from among all those over six feet tall, what is the probability that the
student is a woman?
( A cdot frac{3}{11} )
В. ( frac{5}{11} )
( c cdot frac{7}{11} )
D. none of these
12
922Two cards are drawn simultaneously
from a well shuffled pack of 52 cards.
The expected number of aces is?
( ^{A} cdot frac{1}{221} )
в. ( frac{3}{131} )
c. ( frac{2}{113} )
D. ( frac{1}{131} )
12
923Find ( boldsymbol{A} ) or ( boldsymbol{B} )12
924In bridge game of playing cards, 4 players are distributed one card each
by turn so that each player gets 13 cards. Find out the probability of a
specified player getting a black ace and
a king.
This question has multiple correct options
A ( cdot p=frac{82251}{978775} )
В. ( quad p=frac{164502}{978775} )
C ( quad p=frac{329004}{978775} )
D. ( _{p}=frac{82251}{1957550} )
12
925The probability of student ( A ) passing an examination is ( 2 / 9 ) and of students, ( B ) passing is ( 5 / 9 . ) Assuming the two
events: ( A ) passes’. ( B ) passes’ as independent, find the probability of only
( A ) passing the examination
12
926A bag contains 7 white, 5 black and 4
red balls. Four balls are drawn without
replacement. Find the probability that at least three balls are black.
12
927The probability that ( A ) can solve a problem is ( frac{2}{3} ) and that ( B ) can solve is ( frac{3}{4} ) If both of them attempt the problem. What is probability that the problem act solved?
A ( cdot frac{11}{12} )
в. ( frac{7}{12} )
c. ( frac{5}{12} )
D. ( frac{9}{12} )
12
928Find the probability of drawing a white ball from a box containing 3 white and 5 black balls12
929In a race of 12 cars, the probability that ( operatorname{car} A ) will win is ( frac{1}{5} ) and of ( operatorname{car} B ) is ( frac{1}{6} )
and that of car ( C ) is ( frac{1}{3} . ) Find the probability that only one of them won the race.
12
930A die of six faces marked with the
integers 1,2,3,4,5,6 one on each face Is thrown twice in succession what is
the total number of outcomes thus
obtained?
12
931A fair coins is tossed 8 times. Find the
probability that:
(i) it shows no head
(ii) it shows head at least once.
12
932One mapping is selected at random from all the mappings of the set ( A= ) ( mathbf{1}, mathbf{2}, mathbf{3}, dots, boldsymbol{n} ) into itself. The probability
that the mapping selected is one to one, is given by
A ( cdot frac{1}{n^{n}} )
в. ( frac{1}{n !} )
c. ( frac{(n-1) !}{n^{n-1}} )
D. None of these
12
933A dies is thrown three times and the
sum of three numbers obtained is 15
The probability of first throw being 5 is:
A ( cdot frac{3}{10} )
B. ( frac{2}{5} )
c. ( frac{1}{5} )
D. ( frac{4}{5} )
12
934A die if thrown once. Find the probability
of getting a number less than 5
12
935Two dice are thrown simultaneously.
The probability of getting a multiple of 2 on one die and a multiple of 3 on the other is
A ( cdot frac{5}{36} )
в. ( frac{5}{12} )
c. ( frac{11}{36} )
D. ( frac{1}{12} )
12
936( mathrm{X}^{prime} ) speaks truth in ( 60 % & ) ‘y’ is ( 50 % ) of the cases. The probability that they contradict each other while narrating
the same incident, is
A ( cdot frac{1}{2} )
в. ( frac{1}{8} )
( c cdot frac{1}{4} )
D.
12
937A die has six faces numbered from 1 to
6. It is rolled and number on the top face is noted. When this is treated as
random trial.
(a) What are the possible outcomes?
(b) Are they equally likely? Why?
(c) Find the probability of a composite number turning up on the top face.
12
938If ( P(n) ) is the statement ” ( n^{2} ) is even”,
then what is ( boldsymbol{P}(boldsymbol{3}) ) ?
12
939A pair of unbiased dice is rolled
together till a sum is either 5 or 7 is
obtained, The probability that 5 comes
before 7 is
A . ( 2 / 5 )
в. ( 3 / 5 )
c. ( 4 / 5 )
D. none of these
12
940( A ) and ( B ) are events such that ( p(A cup )
( boldsymbol{B})=mathbf{3} / mathbf{4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}(overline{boldsymbol{A}})=frac{mathbf{2}}{mathbf{3}} )
( operatorname{then} P((bar{A} cap B) ) equals
A ( cdot frac{5}{12} )
B. ( frac{3}{8} )
( c cdot frac{4}{5} )
( D cdot frac{5}{4} )
12
941The probability of drawing a red 9 from a standard pack of 52 playing cards is
A ( cdot frac{1}{13} )
в. ( frac{1}{26} )
( c cdot frac{1}{2} )
D. ( frac{1}{4} )
12
942If ( P(E)=0 ) then ( E ) is a/an
A. sure event
B. impossible event
c. equally likely event
D. none of these
12
943In figure points ( A, B, C ) and ( D ) are the
centre of four circles that each have a
radius of length one unit. If a point is
selected at random from the interior of
square ABCD.What is the probability
that the point will be chosen from the
shaded region?
A ( cdotleft(1-frac{pi}{4}right) )
в. ( left(1-frac{pi}{2}right) )
( c cdotleft(1-frac{pi}{6}right) )
D. ( left(2-frac{pi}{4}right) )
12
944For a biased die the probabilities for the different faces to turn up are given
below:
The die is tossed and you are told that either face one or face two turned up.
Then the probability that it is face one
is.
Faces:
Probabilities: ( quad ) 0.1 ( quad ) 0.32 ( quad ) 0.21
A. ( 1 / 6 )
в. ( 1 / 10 )
c. ( 5 / 49 )
D. ( 5 / 21 )
12
945The mean score of 1000 students for an
examination is 34 and ( S . D . ) is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) determine the limit of the marks of
the central ( 70 % ) of the candidates:
( {boldsymbol{P}[mathbf{0}<boldsymbol{z}<mathbf{0 . 2 5}]=mathbf{0 . 0 9 8 7} boldsymbol{P}[mathbf{0}<boldsymbol{z}<mathbf{1} )
12
9465 cards are drawn at random from a well
shuffled pack of 52 playing cards. If it is known that there will be at least 3
hearts, the probability that all the 5 are hearts is
A ( cdot frac{13}{^{52} C_{5}} )
в.
c.
D. ( frac{^{13} C_{5}}{^{13} C_{3} times^{13} C_{4} times^{13} C_{5}} )
12
947If ( Pleft(E_{k}right) propto k ) for ( 0 leq k leq n, ) the ( P(A) )
equals
A. ( 3 n /(4 n+1) )
B. ( (2 n+1) / 3 n )
c. ( 1 /(n+1) )
D. ( 1 / n^{2} )
12
948fthe binomial distribution whose mean
is 5 and variance ( frac{10}{3} ) is ( P(X=r)= )
( ^{15} C_{r}left(frac{1}{a}right)^{r}left(frac{2}{a}right)^{15-r}, r=0,1,2, dots, 15 )
then the value of ( a ) is
12
949Probability of an event always greater
than or equal to
A ( cdot frac{1}{2} )
B. 1
c. 0
D. –
12
950There is ( 25 % ) chance that it rains on any
particular day. What is the probability that there is at least one rainy day within a period of 7 days?
( ^{A} cdot_{1-}left(frac{1}{4}right)^{7} )
B. ( left(frac{1}{4}right)^{7} )
( ^{c}left(frac{3}{4}right)^{7} )
D. ( _{1-}left(frac{3}{4}right)^{7} )
12
951Wher
distribution of 2 black and 2 white balls
in two containers are as shown.Which
of the following statements is true?
A. (iv) has the maximum possibility of picking a black ball
B. (i) and (iv) has equal probability of picking a white ball
C. (iii) has the maximum possibility of picking a white ball
D. (ii) has the maximum possibility of picking a white ball
12
952The number of ways of arranging the letters ( A A A A A, B B B, D, E E & F ) in a row
if the letter ( C ) are separated from one another is
( mathbf{A} cdot_{13} s_{3} cdot frac{12 !}{5 ! 3 ! 2 !} )
в. ( frac{13 !}{5 ! 3 ! 2 !} )
c. ( frac{14 !}{3 ! 32 !} )
D. none
12
953In a certain city two newspapers ( A ) and
( B ) are published. It is known that ( 25 % ) of
the city population reads ( A ) and ( 20 % ) of
the population reads ( B .8 % ) of the
population reads both ( A ) and ( B ). It is
known that ( 30 % ) of those who read ( A ) but
not ( B ) look into advertisements and ( 40 % )
of those who read ( B ) but not ( A ) look
advertisements while ( 50 % ) of those who
read both ( A ) and ( B ) look into
advertisements. What is the
percentage of the population who reads an advertisement?
A ( cdot frac{139}{500} )
в. ( frac{361}{500} )
c. ( frac{139}{1000} )
D. ( frac{861}{1000} )
12
954If ( x ) is a binomial variable with ( P=frac{1}{4} ) then the smallest value of ( n ) so that
( P(x geq 1)>0.70 ) is
A . 3
B. 4
( c .5 )
D. 6
12
955A number is selected at random from
the first 1,000 natural numbers. What is the probability that the number so
selected would be a multiple of 7 or ( 11 ? )
A . 0.25
B. 0.32
c. 0.23
D. 0.33
12
956Two dice are thrown sumiltaneously.
Find the probability that the sum of the
numbers on the faces is not divisible by 4 or divisible by 5
12
957A card is drawn from a well shuffled
pack of 52 cards. Events A and B are defined as follows:
( A: ) Getting a card of spade
B : Getting an ace, then ( A ) and ( B ) are
A. mutually exclusive and independent events
B. not mutually exclusive but independent events
c. mutually exclusive and not independent events
D. neither mutually exclusive nor independent events
12
958Assertion
At the college entrance examination
each candidate is admitted or rejected
according to whether he has passed or failed the tests. Of the candidates who
are really capable, ( 80 % ) pass the test
and of the incapable, ( 25 % ) pass the test.
Given that ( 40 % ) of the candidates are
really capable, then the proportion of
capable college students is about ( 68 % )
Reason
( Pleft(frac{A}{B}right)=frac{P(A) Pleft(frac{B}{A}right)}{P(A) Pleft(frac{B}{A}right)+Pleft(A^{prime}right) Pleft(frac{B}{A^{prime}}right)} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
12
959Tossing a coin is an example of
A. space
в. sample
c. experiment
D. event
12
960If ( A ) and ( B ) are events such that ( P(A)= ) ( frac{3}{8}, P(B)=frac{5}{8} ) and ( P(A cup B)=frac{3}{4}, ) then
( Pleft(frac{A}{B}right)= )
( A cdot frac{2}{3} )
B. ( frac{2}{5} )
( c cdot frac{1}{3} )
D.
12
961Assertion
In rolling a dice, the probability of getting number 8 is zero.
Reason

Its an impossible event.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

12
9629.
Numbers 1 to 5 are written on separate slips, i.e one number
on one slip and put in a box. Wahida pick a slip from the box
without looking at it. What is the probability that the slip
bears an odd number?
11
963Two coins are available, one fair and the
other two-headed. Choose a coin and
toss it once; assume that the unbiased coin is chosen with probability ( frac{3}{4} . ) Given that the outcome is head the probability that the two-headed coin was chosen, is
A.
в. ( frac{2}{5} )
( c cdot frac{1}{5} )
D.
12
964Two cards are drawn with replacement
from a well shuffled deck of 52 cards.
Find the mean and variance for the
number of aces
12
965Find the number of ways in which a lady
can invite 6 guests selected from 10
friends so that two of the friends will not
attend the party together ?.
12
966Which of the following is not true?
A ( cdot P_{700}>2 / 3 )
В. ( P_{101}2 / 3 )
D. none of these
12
967The probability that it will rain on a
particular day is 0.64 what is the probability that it will not rain on that day?
12
968Find the probability of scoring a total of more than ( 7, ) when two dice are thrown
A ( .5 / 12 )
B. ( 5 / 18 )
( c .5 / 6 )
D. ( 5 / 24 )
12
969(i) ( A ) lot of 20 bulbs contain 4 defective
ones. One bulb is drawn at random from
the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in
(i) is not
defective and not replaced. Now bulb is drawn at random from the rest. What is
the probability that thisbulb is not defective?
12
970If ( A, B ) and ( C ) are three events such that
( boldsymbol{P}(boldsymbol{B})=frac{1}{2} ; boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}^{prime}right)=frac{1}{3} ) and
( boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B} cap boldsymbol{C}^{prime}right)=frac{1}{336} operatorname{then} boldsymbol{P}(boldsymbol{B} cap boldsymbol{C}) ) is
equal to ( dots )
A ( cdot frac{328}{2016} )
в. ( frac{330}{2016} )
c. ( frac{324}{2016} )
D. ( frac{320}{2016} )
12
971The distance (in ( mathrm{km} ) ) of 40 engineers from their residence to their place of
work were found as follows:
[
begin{array}{ccccccccc}
5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 \
19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 \
7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18
end{array}
]
( begin{array}{llllll}mathbf{1 2} & mathbf{1 4} & mathbf{2} & mathbf{9} & mathbf{6} & mathbf{1 5}end{array} ) 15
[
7
]
What is the empirical probability that an engineer lives:
(i) less than ( 7 k m ) from her place of
work?
(ii) more than or equal to ( 7 k m ) from her
place of work?
(iii) within ( frac{1}{2} k m ) from her place of work?
12
972If ( A ) and ( B ) are two events such that
( P(A)=frac{3}{8}, P(B)=frac{5}{8} ) and
( P(A cup B)=frac{3}{4}, ) then ( P(A cap bar{B})= )
( A cdot frac{5}{8} )
B. ( frac{3}{8} )
( c cdot frac{1}{8} )
D.
12
973There are 15 tickets in a box, each
bearing one of the numbers from 1 to 15 One ticket is drawn from the box. Find
the probability of event that the ticket drawn –
(1) shows an even number.
(2) shows a number which is a multiple
of 5.
12
974A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn
at random. The probability that they are not of same colour is
( ^{mathrm{A}} cdot frac{37}{44} )
в. ( frac{31}{44} )
c. ( frac{21}{44} )
D. ( frac{41}{44} )
12
975Let ( X ) be a random variable which
assumes values ( x_{1}, x_{2}, x_{3}, x_{4} ) such that
( mathbf{2} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{1}right)=mathbf{3} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{2}right)=boldsymbol{P}(boldsymbol{X}= )
( left.boldsymbol{x}_{3}right)=mathbf{5} boldsymbol{P}left(boldsymbol{X}=boldsymbol{x}_{4}right) )
Find the probability distribution of ( boldsymbol{X} )
12
976How many five letters words can be
formed using the letter ( boldsymbol{T} boldsymbol{I} ) MRET?
12
977Two coins are tossed. Find the
conditional probability that two Heads will occur given that at least one occurs
A ( cdot frac{1}{3} )
B. ( frac{1}{2} )
( c cdot frac{1}{4} )
D. none of these
12
978A natural number ( x ) is chosen at
random from the first 120 natural
numbers and it is observed to
be divisible by 8 , then the probability that it is not divisible by 6 is
( A cdot frac{1}{3} )
B.
( c cdot frac{3}{4} )
D. ( frac{2}{3} )
12
979If ( A ) and ( B ) are independent events with
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5 .} ) then find
( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) )
12
980Let ( X ) and ( Y ) be two events such that
( P(X)=frac{1}{3}, P(X / Y)=frac{1}{2} ) and
( boldsymbol{P}(boldsymbol{Y} / boldsymbol{X})=frac{2}{5} cdot ) Then
This question has multiple correct options
( ^{mathbf{A}} cdot P(X cup Y)=frac{2}{5} )
В ( cdot P(Y)=frac{4}{15} )
( c cdot Pleft(X^{prime} mid Yright)=frac{1}{2} )
D. ( P(X cap Y)=frac{1}{5} )
12
981Let ( S_{n}=sum_{k=1}^{n} k ) denote the sum of the
first ( n ) positive integers. The numbers
( boldsymbol{S}_{1}, boldsymbol{S}_{2}, boldsymbol{S}_{3}, ldots, boldsymbol{S}_{99} ) are written on ( boldsymbol{9 9} )
cards. The probability of drawing a card with an even number written on it is
A ( cdot frac{1}{2} )
в. ( frac{49}{100} )
c. ( frac{49}{99} )
D. ( frac{48}{99} )
12
982toppr LoGin
Q Type your question
to Rs. ( 50,000 . ) The data about the
number of persons in various
categories is as under:

Monthly ( quad ) Number of Cars income
(in rupees) 2 More than
30,001
40,000 If 400 50 25
( 40,001- )
50,000 ( 100 quad 300 ) 125
Find the probability that a person
selected at random in the income slab
( 40,001-50,000 ) have more than 2
cars.
A. 0.125
B. 0.225
c. 0.325
D. None of thesee

12
983The probability that at least one of the events ( A ) and ( B ) occurs is ( frac{3}{5} . ) If ( A ) and ( B ) occur simultaneously with probability ( frac{1}{5} operatorname{then} Pleft(A^{prime}right)+Pleft(B^{prime}right) ) is
A ( cdot frac{2}{5} )
B. ( frac{4}{5} )
( c cdot frac{6}{5} )
D.
12
984Two students Anil and Ashima
appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima
will qualify the examination is 0.10 . The probability that both will quailfy the examination is 0.02 . Find the
probability that
(a) Both Anil and Ashima will not
qualify the examination. (N)
(b) Atleast one of them will not qualify the examination. (N)
(c) Only one of them will qualify the examination. (N)
12
985There are two urns. There are ( m ) white ( & )
( boldsymbol{n} ) black balls in the first urn and ( boldsymbol{p} ) white
& ( q ) black balls in the second urn. One
ball is taken from the first urn & placed
into the second. Now, the probability of drawing a white ball from the second
urn is
A ( cdot frac{p m+(p+1) n}{(m+n)(p+q+1)} )
B. ( frac{(p+1) m+p n}{(m+n)(p+q+1)} )
c. ( frac{q m+(q+1) n}{(m+n)(p+q+1)} )
D. ( frac{(q+1) m+q n}{(m+n)(p+q+1)} )
12
986If ( A & B ) are two events such that
( P(B) neq 1, B^{C} ) denotes the event
complementary to B, then This question has multiple correct options
( ^{mathbf{A}} cdot Pleft(A / B^{C}right)=frac{P(A)-P(A cap B)}{1-P(B)} )
B . ( P(A cap B) geq P(A)+P(B)-1 )
C . ( P(A)>

<P(A) )
D cdot ( Pleft(A / B^{C}right)+Pleft(A^{C} / B^{C}right)=1 )

12
98726. Let A and B be two events such that P(AUB)
6′
P(ANB) = 2 and P(A) = 4, where A stands for the
complement of the event A. Then the events A and B are
(JEEM 2014]
(a) independent but not equally likely.
(6) independent and equally likely.
(c) mutually exclusive and independent.
(d) equally likely but not independent.
12
988Two persons appear for an interview.Probability of their selection ( operatorname{are} frac{1}{4} ) and ( frac{1}{6} ) respectively. Find the probability that none of them gets selected.12
989The probability distribution of a random variable is given below:
[
begin{array}{llll}
boldsymbol{X}=boldsymbol{x} & 0 & 1 & 2 \
P(X= & 0 & K & 2 K
end{array}
]
( 2 k quad 3 K )
[
x)
]
[
text { Then } boldsymbol{P}(mathbf{0}<boldsymbol{X}<mathbf{5})=
]
A ( cdot frac{1}{10} )
B. ( frac{3}{10} )
( c cdot frac{8}{10} )
D. ( frac{7}{10} )
12
990Two mutually exclusive events are always independent always.
A. True
B. False
12
991A coin is tossed 40 times and it showed
tail 24 times.The probability of getting a head was:
A ( cdot frac{2}{5} )
B. ( frac{3}{5} )
( c cdot frac{1}{2} )
D. ( frac{17}{40} )
12
9921
P
lus.
7.
A bag contains 5 red balls, 8 white balls, 4 green balls and
7 black balls. If one ball is drawn at random, find the
probability that it is:
(i) black (ii)red (iii) not green
11
993( boldsymbol{P}(boldsymbol{A})=frac{1}{boldsymbol{Z}} )
( boldsymbol{P}(boldsymbol{B})=frac{1}{boldsymbol{4}} )
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{1}{mathbf{5}} )
( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=? )
12
994Assume that a factory has two
machines ( A ) and ( B ). Past records shows
that machine ( A ) produces ( 60 % ) of the
items of output and machine ( boldsymbol{B} ) produces ( 40 % ) of the items. Further, ( 2 % ) of the items produced by machine ( boldsymbol{A} )
were defective and only ( 1 % ) produced by
machine ( B ) were defective. If a detective
item is drawn at random, what is the
probability that it was produced by machine ( boldsymbol{A} ) ?
12
995‘X’ speaks truth in ( 60 % ) of the cases and
‘Y’ in ( 50 % ) of the cases. The probability that they contradict each other while narrating the some incident, is
A ( cdot frac{1}{2} )
B. ( frac{3}{4} )
( c cdot frac{3}{5} )
D. None of these
12
996The score of the player placing II was
A ( cdot 5 frac{1}{2} )
в. ( 6 frac{1}{2} )
( c cdot 6 )
D. ( operatorname{can}^{prime} t ) say
12
997toppr
Q Type your question
( A_{1}= ) last digit of the product is not the
number 1,3,7 or 9
( A_{2}= ) last digit of the product is among
the number 1,3,5,7 or 9
( A_{3}= ) last digit of the product is among the number 1,3,7 or 9
( A_{4}= ) last digit of Ihe product ‘is among
the number 2,4,6 or 8
( A_{5}= ) last digit of the product is the
number 5.
( A_{6}= ) last digit of the product is the
number 0
( A_{7}= ) last digit of the product is
1,2,3,4,6,7,8 or ( 9.0 n ) the basis of above information answer the following
questions. The chance that last digit of the product
is ( boldsymbol{A}_{3} )
( ^{mathrm{A}} cdotleft(frac{3}{5}right)^{prime} )
B. ( left(frac{2}{5}right)^{n} )
( ^{c} cdotleft(frac{2}{3}right)^{n} )
D. ( left(frac{4}{5}right)^{prime} )
12
998If ( P(E) ) denotes the probability of an event ( mathrm{E} ), then
A. ( P(E)1 )
c. ( 0 leq P(E) leq 1 )
D. ( -1 leq P(E) leq 1 )
12
999The probability of an event which is sure to occur at every performance of an experiment is called a
A. simple event
B. compound event
c. complementary event
D. certain event
12
1000A family has three children. Event ( A ) is
that family has at most one boy, Event
( B^{prime} ) is that family has at least one boy
and one girl, Event ( ^{prime} C^{prime} ) is that the family has at most one girl. Find whether
events ( ^{prime} A^{prime} ) and ( ^{prime} B^{prime} ) are independent. Also find whether ( A, B, C ) are independent or
not
12
1001A coin is tossed 150 times and the
outcomes are recorded. The frequency distribution of the outcomes ( H ) (i.e.,
head) and ( T ) (i.e., tail) is given below :
Outcome
[
begin{array}{ll}
boldsymbol{H} & boldsymbol{T} \
& \
85 & 65
end{array}
]
Frequency
Find the value of ( P(H) ), i.e., probability of
getting a head in a single trial.
( mathbf{A} cdot P(H)=0.769(text { approx }) )
B . ( P(H)=0.663 ) (approx)
( mathbf{c} cdot P(H)=0.567(text { approx }) )
D. None of these
12
1002The probability that ( A ) hits a target is ( frac{1}{3} ) and the probability that ( B ) hits it, is ( frac{2}{5} ) What is the probability that the target
will be hit, if each one of ( A ) and ( B ) shoots
at the target?
12
1003A bag contains four tickets marked
with ( 112,121,211,222, ) one ticket is
drawn at random from the bag. Let
( boldsymbol{E}_{i}(boldsymbol{i}=mathbf{1}, mathbf{2}, mathbf{3}) ) denote the event that ( boldsymbol{i}^{t h} )
digit on the ticket is 2 then :
This question has multiple correct options
A ( . E_{1} ) and ( E_{2} ) are independent
B. ( E_{2} ) and ( E_{3} ) are independent
C ( . E_{3} ) and ( E_{1} ) are independent
D. ( E_{1}, E_{2}, E_{2} ) are independent
12
1004A fair coin is tossed five times. If the out
comes are 2 heads and 3 tails (in some
order), then what is the probability that the fourth toss is a head?
A ( cdot frac{1}{4} )
B. ( frac{2}{5} )
( c cdot frac{1}{2} )
D. ( frac{3}{5} )
12
1005Which of the following are equally likely outcomes?
A. Tossing a coin getting head or tail
B. While throwing a die getting any one of 6 numbers
c. Both A and B
D. None of these
12
1006Suppose Mr. Ramesh have rupee 2,3
and 5 notes. In howmany ways he can
get a sum of rupees 83 such that atleast one note of each type is present and the number of 2 rupee note(s) is less than number of 3 rupee note(s) which is again less than the number of
5 rupees note ( (s) )
A . 8
B. 9
c. 10
D. 12
12
1007A fair coin is tossed 100 times. The
probability of getting tails an odd number of times is
A ( cdot frac{1}{2} )
B. ( frac{1}{4} )
c. ( frac{1}{8} )
D. ( frac{3}{8} )
12
1008The number of ways in which 10
candidates ( A_{1}, A_{2}, dots, A_{10} ) can be
ranked so that ( A_{1} ) is always above ( A_{2} )
is:-
A ( cdot frac{10 !}{2} )
B . ( 2^{7} 3^{4} 5^{2} 7^{1} )
( mathbf{c} cdot 2^{8} 5^{2} )
D. ( 3^{4} 5^{2} 7 )
12
1009If two events ( A ) and ( B ) such that ( Pleft(A^{c}right) )
( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}left(boldsymbol{A B}^{c}right)=mathbf{0 . 5}, ) then
( boldsymbol{P}left[boldsymbol{B} /left(boldsymbol{A} cup boldsymbol{B}^{c}right)right]= )
A . 0.25
B. 0.50
c. 0.75
D. None of these
12
1010For the numbers in the list, write down
(a) the range
(b) the mode
(c) the median
12
1011If ( X ) is normally distributed with mean 6 and standard deviation ( 5, ) find:
(i) ( boldsymbol{P}[mathbf{0} leq boldsymbol{X} leq mathbf{8}] )
(ii) ( boldsymbol{P}(|boldsymbol{X}-mathbf{6}|<mathbf{1 0}) )
Here ( boldsymbol{P}(mathbf{0}<boldsymbol{Z}<mathbf{1} . mathbf{2})=mathbf{0 . 3 8 4 9} )
( boldsymbol{P}(mathbf{0}<Z<mathbf{0 . 4})=mathbf{0 . 1 5 5 4} )
( boldsymbol{P}(mathbf{0}<boldsymbol{Z}<mathbf{2})=mathbf{0 . 4 7 7 2} )
12
1012State and prove Bayes’ theorem12
1013It has been found that if ( A ) and ( B ) play a game 12 times, ( A ) wins 6 times, ( B ) wins 4
times and they draw twice. A and B take
part in a series of 3 games. The probability that they win alternately, is :
A ( cdot frac{5}{12} )
в. ( frac{5}{36} )
c. ( frac{19}{27} )
D. ( frac{5}{27} )
12
1014A die is thrown. Write the sample space.
If ( B ) is the event of getting an even number, write the event ( B ) using set
notation.
12
1015In a simultaneous throw of a pair of
dice, if the probability of getting a sum less then 6 is ( frac{5}{a} . ) Find ( a )
12
1016A ball is drawn at random from box ( boldsymbol{I} )
and transferred to box ( I I ). If the
probability of drawing a red ball from box ( I, ) after this transfer, is ( frac{1}{3}, ) then the correct option(s) with the possible
values of ( n_{1} ) and ( n_{2} ) is (are)
This question has multiple correct options
A ( cdot n_{1}=4 ) and ( n_{2}=6 )
B . ( n_{1}=2 ) and ( n_{2}=3 )
c. ( n_{1}=10 ) and ( n_{2}=20 )
D. ( n_{1}=3 ) and ( n_{2}=6 )
12
1017A bag contains 10 white, 5 black, 3
green and 2 red balls. One ball is drawn
at random. Find the probability that the ball drawn is white or black or green
12
1018The probability that a marksman will hit a target is given as ( frac{1}{5}, ) then his probability of at least one hit in 10 shots is
( ^{mathrm{A}} cdot_{1}-left(frac{4}{5}right)^{10} )
в. ( frac{1}{510} )
c. ( _{1-frac{1}{5^{10}}} )
D. None of these
12
10191500 families with 2 children were
selected randomly, and the following
data were recorded:
No. of girls in family

No. of families
[
begin{array}{ll}
475 & 814
end{array}
]
Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl
Also check whether the sum of these
probabilities is 1

12
1020If ( A ) and ( B ) are two mutually exclusive
events in a sample space ( S ) such that ( boldsymbol{P}(boldsymbol{B})=2 boldsymbol{P}(boldsymbol{A}) ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{S} ) then
( boldsymbol{P}(boldsymbol{A})= )
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{4} )
D.
12
1021What is the number of outcomes when
a coin is tossed and then a die is rolled
only in case a head is shown on the
coin?
A . 6
B. 7
c. 8
D. None of the above
12
1022Tell whether the following is certain to happen, possible can happen but not certain
Tomorrow will be a cloudy day.
12
1023In a school, there are 1000 student, out
of which 430 are girls. It is known that out of ( 430,10 % ) of the girls study in class ( X I I . ) What is the probability that
a student chosen randomly studies in
class ( X I I ) given that the chosen
student is a girl?.
12
1024Three dice are rolled. The probability that the same number will appear on
each of them is
A ( cdot frac{1}{36} )
B. ( frac{1}{12} )
c. ( frac{2}{49} )
D. None
12
1025Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional
probability that both are girls given that
(i) the youngest is a girl, (ii) at least one is a girl?
A. 0.33,0.34
В. 0.88,0.98
c. 0.78,0.67
D. 0.5,0.33
12
1026The variable which takes some specific values is called
A. discrete random variable
B. continuous random variable
c. both A and B
D. none
12
1027A study was conducted to find out the
concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
( begin{array}{cccccc}0.03 & 0.08 & 0.08 & 0.09 & 0.04 & 0.17 \ 0.16 & 0.05 & 0.02 & 0.06 & 0.18 & 0.20 \ 0.11 & 0.08 & 0.12 & 0.13 & 0.22 & 0.07 \ 0.08 & 0.01 & 0.10 & 0.06 & 0.09 & 0.18 \ 0.11 & 0.07 & 0.05 & 0.07 & 0.01 & 0.04end{array} ) Using this table, find the probability of the concentration of sulphur dioxide in
the interval ( 0.12-0.16 ) on any of these
days.
12
1028In an entrance test is graded on the basis of two examinations, the
probability of a randomly chosen
student passing the first examination
is 0.8 and the probability of passing the second examination is 0.7 . The
probability of passing at least of them is ( 0.95 . ) What is the probability of passing both?
12
1029One number is to be chosen from
Numbers 1 to ( 100, ) the probability that it is divisible by 3 or 7 is…..
A ( frac{33}{100} )
в. ( frac{7}{100} )
c. ( frac{4}{100} )
D. ( frac{43}{100} )
12
1030Two coins are tossed once, where
(i) ( E: ) tail appears on one coin, ( boldsymbol{F}: ) one
coin shows head
(ii) ( E: ) no tail appears, ( boldsymbol{F}: ) no head
appears
Determine ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) )
A .1,0
в. 1,0.2
c. 0,2
D. 1,3
12
1031The probability of event is 0
A. Sure
B. Impossible
c. Exclusive
D. None of these
12
1032An artillery target may be either at point
( I ) with probability ( frac{8}{9} ) or at point ( I I ) with
probability ( frac{1}{9} . ) We have 21 shells each of which can be fired at point ( I ) or ( I I ). Each
shell may hit the target independently of the other shell with probability ( frac{1}{2} . ) How
many shells must be fired at point ( I ) to hit the target with maximum
probability?
A. ( P(A) ) is maximum where ( x=11 ).
B. ( P(A) ) is maximum where ( x=12 )
c. ( P(A) ) is maximum where ( x=14 )
D. ( P(A) ) is maximum where ( x=15 )
12
1033The outcome of each of 30 items was observed; 10 items gave an outcome ( frac{1}{2} ) deach, 10 items gave outcome ( frac{1}{2} ) each
and the remaining 10 items gave outcome ( frac{1}{2}+d ) each. If the variance of this outcome data is ( frac{4}{3} ) then ( |boldsymbol{d}| ) equals:-
A. 2
B. ( frac{sqrt{5}}{2} )
( c cdot frac{2}{3} )
D. ( sqrt{2} )
12
1034If ( A ) and ( B ) are mutually exclusive such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} )
find
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
1035Which one of the following cannot be the probability of an event.
A ( cdot frac{1}{3} )
в. ( frac{11}{36} )
c. ( -frac{2}{3} )
( D )
12
1036Six boys and girls sit in a row randomly Find the probability that the six girls sit together.
A ( cdot p=frac{1}{95040} )
B. ( _{p}=frac{1}{132} )
c. ( _{p}=frac{1}{924} )
D. ( p=frac{1}{66} )
12
1037A coin is tossed 3 times. The probability of getting head and tail alternately is
A ( cdot frac{1}{8} )
B. ( frac{1}{2} )
( c cdot frac{1}{4} )
D.
12
1038( A ) and ( B ) are events with ( P(A)= )
( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3} )
Find the probability that neither ( A ) and ( B ) occurs.
12
1039A card is thrown from a pack of 52 cards
so that each card equally likely to be selected. Then find whether the events
( A ) and ( B ) independent?
( A= ) the card drawn is spade, ( B= ) the card drawn in an ace.
12
1040Three persons ( A, B ) and ( C ) apply for a job of Manager in a Private company. Chance of their selection ( (A, B text { and } C) )
are in the ratio ( 1: 2: 4 . ) The probability
that ( A, B ) and ( C ) can introduce changes to improve profits of company are 0.8,0.5 and 0.3 respectively, if the changes does not take place, find the probability that it is due to the
appointment of ( boldsymbol{C} )
12
1041One hundred identical coins, each with
probability ( p ) of showing heads are
tossed once. If ( 0<p<1 ) and the
probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of ( p ) is
A ( cdot 1 / 2 )
B. ( 51 / 101 )
c. ( 49 / 101 )
D. 3 / 101
12
1042The mean and variance of a binomial
distribution are 4 and 3 respectively. Fix the distribution and find ( P(X geq 1) )
12
1043In a shooting game, John shoots the balls 20 times out of 40 trials. What is
the empirical probability of the
shooting event?
A ( cdot frac{3}{2} )
в. ( frac{1}{2} )
( c cdot frac{5}{2} )
D. ( frac{7}{2} )
12
1044If ( A ) is an event of a random experiment such that ( P(A): P(bar{A})=5: 11 ), then
find ( P(A) ) and ( P(bar{A}) )
12
1045( A ) is known to tell the truth in 5 cases
out of 6 and he states that a white ball
was drawn from a bag containing 8
black and 1 white ball. The probability that the white ball was drawn, is
A ( cdot frac{7}{13} )
B. ( frac{5}{13} )
( c cdot frac{9}{13} )
D. None of these
12
1046The probability of getting a boy in a class is 0.6 and there are 45 students In a class, then find the number of girls in the class.12
1047A player tosses two fair coins. He wins Rs. ( 5 /- ) if two heads occur, ( R s .2 /- ) if one head occurs and ( R s .1 /- ) if no head
occurs. Then his expected gain is
A ( cdot ) Rs. ( frac{8}{3} )
в. ( operatorname{Rs} . frac{7}{3} )
c. ( R s .2 .5 )
D. Rs.1.5
12
1048A letter is known to have come eithe
from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from
London?
A ( cdot frac{12}{17} )
в. ( frac{5}{17} )
c. ( frac{5}{12} )
D. ( frac{7}{12} )
12
1049A fair die is tossed. If 2,3 or 5 occurs, the player wins that number of rupees, but if 1,4 or 6 occurs, the player loses that number of rupees. Then find the possible payoffs for the player.12
1050The probability of an impossible event
is
A .
B. 0
c. less than 0
D. greater than 1
12
1051What is the total number of elementary events associated to the random
experiment of throwing three dice together
12
1052A coin is tossed ( (mathbf{m}+mathbf{n}) ) times ( (mathbf{m}<mathbf{n}) ) The probability for getting atleast 'n consecutive heads is
A ( cdot frac{m+2}{2^{n+1}} )
в. ( frac{n+2}{2^{m+1}} )
c. ( frac{m}{2^{n+1}} )
D. ( frac{(m+1) times(m+2)}{2^{(m+n+1)}} )
12
1053Let ( A ) and ( B ) be independent events with ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=0.5 . ) Then find:
(i) ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B}) )
(ii) ( boldsymbol{P}(boldsymbol{B} mid boldsymbol{A}) )
( (text { iii) } boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
(iv) ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
1054Assuming the balls to be identical except for difference in colors, the number of ways in which one or more
balls can be selected from 10 white, 9
green and 7 black balls is
A. 880
в. 629
( c .630 )
D. 879
12
1055Consider the following statements:
1. If ( A ) and ( B ) are exhaustive events, then
their union is the sample space.
2. If ( A ) and ( B ) are exhaustive events,
then their intersection must be an
empty event. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
12
1056The chance that a person with two dices, the faces of each being numbered 1 to ( 6, ) will throw aces exactly
4 times in 6 trials is
( ^{mathrm{A}} cdotleft(frac{1}{36}right)^{4} )
( ^{mathrm{B}}left(frac{1}{36}right)^{4}left(frac{35}{36}right)^{2} )
( ^{mathbf{c}} cdot_{4} Cleft(frac{1}{36}right)^{4}left(frac{35}{36}right)^{2} )
( ^{mathrm{D}} cdot_{4}^{6} Cleft(frac{1}{36}right)^{2}left(frac{35}{36}right)^{4} )
12
1057If ( boldsymbol{E} ) and ( boldsymbol{F} ) be events in a sample space
such that ( boldsymbol{P}(boldsymbol{E} cup boldsymbol{F})=mathbf{0 . 8}, boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})= )
0.3 and ( P(E)=0.5, ) then ( P(F) ) is
A . 0.6
B.
( c .0 .8 )
D. None
12
1058If ( A ) and ( B ) are mutually exclusive such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} )
find
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
1059The probabilities of three events ( A, B & ) ( C operatorname{are} P(A)=0.6, P(B)=0.4 ) and ( P(C)=0.5 )
If ( P(A cup B)=0.8, P(A cap C)=0.3, P(A cap )
( B cap C)=0.2 & P(A cup B cup C) geq 0.85 )
Find the range of ( mathrm{P}(B cap C) )
B . [0.25,0.35]
c. [0.2,0.3]
D. [0.2,0.4]
12
1060A die is thrown. If ( A ) is the event that the
number on upper face is less than 5
then write sample space and event ( A ) in
set notation.
12
1061An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top card is a king card.
12
1062There are 5 percent defective items in a large bulk of items. The probability that a sample of 10 items will include not more than one defective item is ( left(frac{19^{9} times 29}{20^{x}}right), ) then what is the value of
( boldsymbol{x} )
12
1063An urn contains 2 white and 2 black
balls. A ball is drawn at random. If it is
white it is not replaced into the urn. Otherwise it is replaced along with another ball of same colour. The process
is repeated. The probability that the third ball drawn is black is1 ( -frac{k}{30} ). Find
the value of ( k ) ?
12
1064If ( A ) and ( B ) are independent events of ( a ) random experiment such that ( boldsymbol{P}(boldsymbol{A} cap )
( B)=frac{1}{6} ) and ( P(bar{A} cap bar{B})=frac{1}{3}, ) then ( P(A) )
is equal to
A ( cdot frac{1}{3} )
B. ( frac{2}{3} )
( c cdot frac{5}{7} )
D. None of these
12
1065The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months
and standard deviation of 2 months.
Find the probability that an instrument produced by this machine will last less than 7 months.
A . 0.2316
B. 0.0062
c. 0.0072
D. 0.2136
12
1066A card is drawn from a pack of 52 cards.
The probability of getting a queen of spade or a king of diamond is
A ( cdot frac{1}{56} )
в. ( frac{1}{26} )
c. ( frac{1}{52} )
D. ( frac{3}{56} )
12
1067The probability of the simultaneous occurrence of two events ( A ) and ( B ) is ( p ). If
the probability that exactly one of ( A, B )
occurs is ( boldsymbol{q} ), then This question has multiple correct options
A ( cdot Pleft(A^{prime}right)+Pleft(B^{prime}right)=2+2 q-p )
B . ( Pleft(A^{prime}right)+Pleft(B^{prime}right)=2-2 p-q )
c. ( P(A cap B mid A cup B)=frac{p}{p+q} )
D . ( Pleft(A^{prime} cap B^{prime}right)=1-p-q )
12
1068An unbiased die is thrown again and again until three sixes are obtained. The
probability of obtaining ( 3 mathrm{rd} ) six in the sixth throw of the die is ( frac{1250}{x^{x}} )
12
1069If ( mathrm{E} & mathrm{F} ) are events with ( boldsymbol{P}(boldsymbol{E}) leq boldsymbol{P}(boldsymbol{F}) & )
( boldsymbol{P}(boldsymbol{E} cap boldsymbol{F})>0, ) then?
A. Occurrence of ( E Rightarrow ) occurrence of ( F )
B. Occurrence of F ( Rightarrow ) occurrence of E
c. Non-occurrence of ( E Rightarrow ) non-occurrence of ( F )
D. None of the above implications holds
12
1070Two unbiased dice are thrown. The
probability that the sum of the numbers appearing on the top face of two dice is
greater than 7 if 4 appear on the top face of the first dice is…
A ( cdot frac{1}{3} )
B. ( frac{1}{2} )
c. ( frac{1}{12} )
D.
12
10718.
A glass jar contains 6 red, 5 green, 4 blue and 5 yellow
marbles of same size. Hari takes out a marble from the jar at
random. What is the probability that the chosen marble is
of red colour?
11
1072Mixed/Compound/Composite event12
1073Assertion
If ( A & B ) are two events such that ( P(A)=frac{2}{5}, P(B)=frac{3}{4} ) then ( frac{1}{20} leq )
( P(A cap B) leq frac{2}{5} )
Reason
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) leq max {boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(B)} & )
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) geq min {boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(boldsymbol{B})} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
1074Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is?
A . ( 1 / 6 )
B . ( 1 / 36 )
c. ( 12 / 151 )
D. None of these
12
1075A bag contains cards numbered from 1
to ( 49 . ) A card is drawn from the bag at
random, after mixing the card thoroughly. Find the probability that the number on the drawn card is
(i) an odd number
(ii) a multiple of 5
(iii) a perfect square
(iv) an even prime
number
12
1076Two squares are chosen from the
squares of an ordinary chess board. It is given that the selected squares do not belong to the same row or column. The probability that they have a side in
common
A ( cdot frac{25}{49} )
в. ( frac{32}{49} )
c. ( frac{1}{18} )
D.
12
1077If two events ( A ) and ( B ) are such that
( boldsymbol{P}left(boldsymbol{A}^{prime}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and
( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right)=mathbf{0 . 5}, operatorname{then} boldsymbol{P}left(frac{boldsymbol{B}}{boldsymbol{A} cup boldsymbol{B}^{prime}}right) )
equala
A ( cdot frac{3}{4} )
B.
( c cdot frac{1}{4} )
D.
12
1078If ( P(A)=1, ) then the event ( A ) is known
as
A. Symmetric event
B. Dependent event
c. Improbable event
D. Sure event
12
1079A die is thrown 100 times with
frequency for the outcomes 1,2,3,4,5
and 6 as given this following table Find the probability of getting
Number greater than 5 as an outcome.
12
1080The number of arrangements of the letters of the word BANANA in which two
N’s do not appear adjacently is
A . 40
B. 60
c. 80
D. 100
12
1081Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that one of them is black and other is red.
12
1082There are 2 brothers ( A ) and
B. Probability that ( A ) will pass in exam is ( 3 / 5 ) and that
B will pass in exam is ( 5 / 8 . ) What will be
the probability that only one will pass in the exam?
12
1083The probability’p’ of happening of an
event
A. Can be negative
В. ( 0 leq p leq 1 )
c. can be greater the 1
D. None of these
12
1084Three coins are tossed. Describe
two events ( A ) and ( B ) which are mutually
exclusive.
12
1085If two events ( A ) and ( B ) are such that
( P(A)>0 ) and ( P(B)=1, ) then ( P ) is equal to
A ( cdot_{1-P}left(frac{A}{B}right) )
в. ( _{1-P}left(frac{A^{prime}}{B}right) )
( ^{c} cdot_{1-P}left(frac{A cup B}{B^{prime}}right) )
D. ( Pleft(frac{A}{B^{prime}}right) )
12
1086Tickets numbered 1 to 20 are mixed up
and then a ticket is drawn at random.
What is the probability that the ticket drawn has a number which is a multiple
of 3 or ( 5 ? )
A ( cdot frac{7}{20} )
в. ( frac{8}{20} )
c. ( frac{6}{20} )
D. ( frac{9}{20} )
12
1087( A ) and ( B ) are two candidates seeking
admission in I.I.T. The probability that ( boldsymbol{A} )
is selected is 0.5 and the probability that both ( A ) and ( B ) are selected is
atmost ( 0.3 . ) Is it possible that the probability of ( boldsymbol{B} ) getting selected is ( mathbf{0 . 9} ) ?
If it is possible then enter 1 , else enter 0
12
1088If ( E_{1} ) and ( E_{2} ) are two events such that ( boldsymbol{P}left(boldsymbol{E}_{1}right)=frac{mathbf{1}}{mathbf{4}}, boldsymbol{P}left(boldsymbol{E}_{2}right)=frac{mathbf{1}}{mathbf{2}} ; boldsymbol{P}left(frac{boldsymbol{E}_{1}}{boldsymbol{E}_{2}}right)=frac{mathbf{1}}{mathbf{4}} )
then choose the correct options.
A. ( E_{1} ) and ( E_{2} ) are mutually exclusive
B. ( E_{1} & E_{2} ) are dependent
c. ( E_{1} ) and ( E_{2} ) are independent
D. ( E_{1} ) and ( E_{2} ) are exhaustive
12
1089A number is chosen at random among
the first 120 natural numbers, The probability of the number chosen being
a multiple of 5 or 15 is
A . ( 1 / 5 )
в. 1 18
c. ( 1 / 6 )
D. none of these
12
1090In a random experiment, a fair die is rolled until two fours are obtained in
succession. The probability that the experiment will end in the fifth throw of the die is equal to:
A ( cdot frac{150}{6^{5}} )
в. ( frac{175}{6^{5}} )
c. ( frac{200}{6^{5}} )
D. ( frac{225}{6^{5}} )
12
1091A bag contains four tickets numbered
( 00,01,10,11 . ) Four tickets are chosen at
random with replacement, the probability that the sum of the numbers on the tickets is ( 23, ) is
A ( .3 / 32 )
в. ( 1 / 64 )
c. ( 5 / 256 )
D. ( 7 / 256 )
12
1092A black and a red dice are rolled.
(a) Find the conditional probability of
obtaining a sum greater than ( 9, ) given that the black die resulted in a 5 .
(b) Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4
A. 0.33,0.11
B. 0.51,0.76
c. 0.56,0.43
D. 0.11,0.65
12
1093Find the number of ways in which 5 boys and 5 girls be seated in a row so that no two girls may sit together.12
1094If ( boldsymbol{P}(boldsymbol{E})=mathbf{0 . 8 7}, ) find ( boldsymbol{P}(overline{boldsymbol{E}}) )12
1095Assertion
If ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B})=boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) cdot mathbf{A}, mathrm{B} ) are two non
mutually exclusive events then
( boldsymbol{P}(boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) )
Reason
For non mutually exclusive events
( (A cap B) neq phi ) and ( P(A / B)= )
( frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{B})}, boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=frac{boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})}{boldsymbol{P}(boldsymbol{A})} )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
1096A die is thrown 24 times. If number 4 come up 12 times, the
probability of number 4′ is
The followine data th
K
. Then the value of k is
e m to the model of
2
10
1097From a well shuffied pack of cards one
card is drawn at random. The
probability that the card drawn is an
ace is
A ( cdot frac{1}{13} )
в. ( frac{1}{14} )
c. ( frac{3}{52} )
D. ( frac{1}{26} )
12
1098A throws a coin 3 times. If he get a head all three times, he is to get a reward of Rs.200, on the other hand if he does not
get 3 heads he is to loose Rs.40. He is
expected to win Rs.
A . Rs. 50
B. Rs. (-10)
c. Rs. 35
D. Rs. 10
12
1099Probability cannot be expressed in
A. fraction form
B. ratio form
c. negative form
D. percentage form
12
1100A man is known to speak the truths 3 out of 4 times. He throw a die and report
that it is six. The probability that it is actually a six, is
A ( cdot frac{3}{8} )
B. ( frac{1}{5} )
( c cdot frac{3}{4} )
D. None of these
12
1101A couple has two children,
(i) Find the probability that both children are males, if it is known that at
least one of the children is male.
(ii) Find the probability that both children are females, if ti is known that the elder child is a female.
A. 0.55,0.38
В. 0.33,0.50
c. 0.67,0.78
D. 0.56,0.67
12
1102In a group of 10 people, ( 70 % ) take vitamins. If you randomly choose 2 of them, what is the probability
that neither person selected takes vitamins?
A ( . . .0677 )
в ( ldots .09 )
( c ldots 30 )
D ( ldots 4 )
( E ldots .49 )
12
1103There are three boxes, each containing a different number of light bulbs. The first box has 10 bulbs, of which four are dead, the second has six bulbs, of which one is dead, and the third box has eight bulbs of which three are dead. What is
the probability of a dead bulb being selected when a bulb is chosen at
random from one of the three boxes?
A. ( frac{115}{330} )
В. ( frac{113}{360} )
c. ( frac{113}{330} )
D. None of these
12
1104(a) T6 16 32 16 .
A bag contains 4 red and 6 black balls. A ball is de
random from the bag, its colour is observed and th:
along with two additional balls of the same colour a
turned to the bag. If now a ball is drawn at random fro
bag, then the probability that this drawn ball is red
all is drawna
and this ball
colour are re-
[JEEM 2018
(a) 2
(b) – 2
(c)
(d) To
are raun successively with replacement from
12
1105If ( A ) and ( B ) are two event such that
( P(A)=frac{6}{11}, P(B)=frac{5}{11} ) and ( P(A cup )
( B)=frac{7}{11}, ) find ( P(A r )
( boldsymbol{B}), boldsymbol{P}(boldsymbol{A} / boldsymbol{B}), boldsymbol{P}(boldsymbol{B} / boldsymbol{A}) )
12
1106If ( A, B ) and ( C ) are three events, then
This question has multiple correct options
A ( . P(text { exactly two of } A, B, C text { occur }) leq P(A cap B)+P(B cap )
( C)+P(C cap A) )
B ( . P(A cup B cup C) leq P(A)+P(B)+P(C) )
C. ( P(text { exactly one of } A, B, C text { occur }) leq P(A)+P(B)+ )
( P(C)-P(B cap C)-P(C cap A)-P(A cap B) )
D. ( P(A text { and at least one of } B, C text { occurs }) leq P(A cap B)+ )
( P(A cap C) )
12
110727. A computer producing factory has only two plants T, and
T, Plant T, produces 20% and plant T, produces 80% of
the total computers produced. 7% of computers produced
in the factory turn out to be defective. It is known that
P(computer turns out to be defective given that it is produced
in plant T)
= 10P (computer turns out to be defective given that it is
produced in plant T.),
where P(E) denotes the probability of an event E. A computer
produced in the factory is randomly selected and it does
not turn out to be defective. Then the probability that it is
produced in plant T, is
(JEE Adv. 2016)
-36
75
(a) (b) (c) (d)
noontira inteners y Yand 7
12
1108If ( frac{1+3 p}{3}, frac{1-2 p}{2} ) are probabilities of two mutually exclusive event, then ( p ) lies in the interval
( ^{A} cdotleft[-frac{1}{3}, frac{1}{2}right] )
B ( cdotleft(-frac{1}{2}, frac{1}{2}right) )
( ^{mathbf{C}} cdotleft[-frac{1}{2}, frac{2}{3}right] )
D. ( left(-frac{1}{3}, frac{2}{3}right) )
12
1109In a single throw of three dice, if the
probability of getting a total of 17 or 18 is ( frac{1}{a} . ) Find ( a )
12
1110Two numbers ( b ) and ( c ) are chosen at
random (with replacement) from the
numbers 1,2,3,4,5,6,7,8 and ( 9 . ) The probability that ( x^{2}+b x+c>0 ) for all
( c in boldsymbol{R} ) is ( frac{mathbf{4} k}{81} . ) Find the value of ( boldsymbol{k} ? )
12
1111Bag ( I ) contains 2 blacks and 8 red balls, bag IIcontains 7 black and 3 red balls
and bag ( I I I ) contains 5 black and ( 5 v )
red balls. One bage is chosen at random and a ball is drawn from it which is
found to bered. Find the probability that the ball is drawn from bag ( I I )
12
1112An experiment involves rolling a pair of dice and recording the numbers that come up describe the following events:
( A: ) the sum is greater than 8
( mathrm{B}: 2 ) occurs on either die
( mathrm{C}: ) the sum is at least 7 and a multiple
of 3
Which pairs of these events are mutually exclusive?
12
1113If ( A ) and ( B ) are mutually exclusive
events, then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) ) equals
( mathbf{A} cdot mathbf{0} )
B. ( frac{1}{2} )
c.
D.
12
1114Consider the experiment of throwing a die, if a multiple of 3 comes up, thrown the die again and if any other number comes, toss a coin. Find the conditional
probability of the event ‘the coin shows a tail’, given that ‘at least one die shows
a 3 ‘.
12
1115The probability of student ( A ) passing an examination is ( frac{2}{9} ) and of students, ( B ) passing is ( frac{5}{9} . ) Assuming the two events:
( A ) passes’. ( B ) passes’ as independent, find the probability of both passing the examination.
12
1116( A ) box ( ^{prime} A^{prime} ) contains 2 white, 3 red and 2
black balls. Another box ‘ ( B^{prime} ) contains 4
white, 2 red and 3 black balls. If two
balls are drawn at random, without
replacement, from a randomly selected box and one ball turns out to be white
while the other ball turns out to be red,
then the probability that both balls are
drawn from box’ ( B^{prime} ) is
A ( cdot frac{7}{16} )
в. ( frac{9}{32} )
( c cdot frac{7}{8} )
D. ( frac{9}{16} )
12
1117For two events ( boldsymbol{A} ) and ( boldsymbol{B}, ) if ( boldsymbol{p}(boldsymbol{A})= )
( boldsymbol{p}(boldsymbol{A} mid boldsymbol{B})=frac{1}{4} ) and ( boldsymbol{p}(boldsymbol{B} mid boldsymbol{A})=frac{1}{2}, ) then
( Pleft(frac{bar{B}}{bar{A}}right)=frac{m}{n} ) where ( m+n= )
12
1118The probability that an event A happens in one trial of an
experimentis 0.4. Three independent trials of the experiment
are performed. The probability that the event A happens at
least once is
(1980)
(a) 0.936 (b) 0.784 (c) 0.904 (d) none of these
т с
12
1119In 16 throws of a die getting an even
number is considered a success, then
the variance of the success is
A . 4
B. 6
( c cdot 2 )
D. 256
12
1120паре спасtwoo пооооп и по
In 65 throws of a dice, 5 is obtained 22 times. Now, in a
22
random throw of a dice, the probability of getting 5 is a
11
1121If heads means one and tail means two,
then coefficients of quadratic equation
( a x^{2}+b x+c=0 ) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A ( cdot frac{5}{8} )
B. ( frac{3}{8} )
( c cdot frac{7}{8} )
D.
12
1122There are 44 students in class ( X ) of ( a )
school of whom 32 are boys and 12 are girls. The class teacher has to select one student as a class representative. He writes the name of each student on a
separate card, the cards being identical. Then he puts cards in a bag
and stir them thoroughly. He then draws one card from the bag. What is the probability that the name written on the card is the name of a girl?
A ( cdot frac{1}{11} )
B. ( frac{5}{11} )
( c cdot frac{7}{11} )
D. None of these
12
1123Arun and Tarun appeared for an
interview for two vacancies. The
probability of Arun’s selection is ( frac{1}{4} ) and that of Tarun’s rejection is ( frac{2}{3} . ) Find the probability that at least one of them will
be selected.
12
1124Two numbers are selected at random
from integers 1 through ( 9 . ) If the sum is even, find the probability that both the
numbers are odd.
12
1125The terms ‘chance’ and ‘probability’ are
synonymous.
A . True
B. False
c. Both
D. None of above
12
1126If a fair die is rolled 4 times, then what is
the probability that there are at least 2
sixes?
A ( cdot frac{19}{144} )
в. ( frac{25}{216} )
c. ( frac{125}{216} )
D. ( frac{175}{216} )
12
1127Two different dice are tossed together.
Find the probability of the sum of no’s appearing on two dice is 5
A ( cdot frac{1}{36} )
в. ( frac{1}{18} )
c. ( frac{1}{9} )
D. ( frac{1}{6} )
12
1128A person writes letters to six friends
and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wring envelope.
12
1129Given that the two numbers appearin
the probability of the event ‘the sum
12
1130Choosing a marble from a jar and landing on heads after tossing a coin is
an act of
A. experiment
B. space
c. sample
D. event
12
1131A random variable ( boldsymbol{X} ) is binomially
distributed with mean 12 and variance
8. The parameters of the distribution
are ( ldots . . & ldots . )
A ( cdot_{36, frac{2}{3}} )
в. ( _{36, frac{1}{3}} )
c. ( _{24, frac{1}{3}} )
D. ( 24, frac{2}{3} )
12
1132If two coins are tossed, then find the
probability of the event that at the most one tail turns up.
12
1133Probability is 0.45 that a dealer will sell
at least 20 television sets during a day, and the probability is 0.74 that he will
sell less that 24 televisions. The
probability that he will sell 20,21,22 or
23 televisions during the day, is
A . 0.19
в. 0.32
c. 0.21
D. None of these
12
1134What is the total number of candidates
at an examination, if ( 31 % ) fail and the
number of failing students is 248
A. 800
B. 900
c. 1,000
D. 1,100
12
1135Suppose a girl throws a die. If she gets a
5 or ( 6, ) she tosses a coin 3 times and
notes the number of heads. If she gets
1,2,3 or 4 she tosses a coin once and notes whether a head or tail is obtained.
If she obtained exactly one head, what
is the probability that she threw 1,2,3
or 4 with the die?
( mathbf{A} cdot frac{1}{9} )
в. ( frac{5}{16} )
c. ( frac{2}{13} )
D. ( frac{8}{11} )
12
1136A bag contains a certain number of
balls, some of which are white;a ball is drawn and replaced, another is then drawn and replaced’ and so on. If p be the chance of white balls that is most
likely to have been drawn in n trials. For
( p=frac{1}{2} ) and ( n=12, ) the number of white
balls required to be drawn is ( k ). Find the
value of ( k )
12
1137A box contains 20 cards marked with
numbers 1 to ( 20 . ) One card os drwan
from the box at random. What is the
probability of the following events:
(1) That number on the card is a prime number,
(2) The number on the card is a perfect
square.
12
1138The probability that a student is not a swimmer is ( frac{1}{5} . ) Then the probability that out of five students, four are swimmers
is
( ^{mathbf{A}} cdot_{^{5}} C_{4}left(frac{4}{5}right)^{4} frac{1}{5} )
( ^{mathrm{B}}left(frac{4}{5}right)^{4} frac{1}{5} )
( ^{mathbf{c}} cdot_{^{5}} C_{1} frac{1}{5}left(frac{4}{5}right)^{4} )
D. none of these.
12
1139If ( A ) and ( B ) are two events such that
( boldsymbol{A} subset boldsymbol{B} ) and ( boldsymbol{P}(boldsymbol{B}) neq 0, ) then which of the
following is correct? This question has multiple correct options
( ^{mathbf{A}} cdot p(A mid B)=frac{P(B)}{P(A)} )
B cdot ( P(A mid B)<P(A) )
C ( cdot P(A mid B) geq P(A) )
D. None of these
12
1140If a random variable X takes values
( (-1)^{k} 2^{k} / k ; k=1,2,3, dots . ) with
probabilities ( boldsymbol{P}(boldsymbol{X}=boldsymbol{k})=frac{mathbf{1}}{mathbf{2}^{k}} ) then
( E(X)= )
A ( . log 2 )
в. ( log e )
c. ( log left(frac{1}{2}right) )
D. ( log left(frac{1}{4}right) )
12
1141Two dice are thrown together. Find the
probability of getting a sum equal to 8
12
1142An die is tossed twice. Find the
probability of getting 4,5 or 6 on the toss and 1,2,3 or 4 on the second toss.
12
1143Two cards are drawn from a well
shuffled pack of 52 cards. Find the
probability distribution of the number of aces.
12
1144Let ( X ) represent the difference between
the number of heads and the number of
tails obtained when a coin is tossed 6
times. What are possible values of ( X ? )
в. 0,2,4,6
c. 6,7,7,2
D. 6,4,2,0
12
1145Consider two events ( A ) and ( B ) of an
experiment where ( P(A cap B)=frac{1}{4} ) and ( P(B)=frac{1}{2}, ) then ( P(A) ) cannot exceed
( A cdot frac{1}{2} )
B. ( frac{2}{3} )
( c cdot frac{3}{4} )
D.
12
1146Suppose ( 5 % ) of men and ( 0.25 % ) of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal
number of males and females.
12
1147An event ( X ) can take place in
conjunction with any one of the mutually exclusive and exhaustive events ( A, B ) and ( C . ) If ( A, B, C ) are equiprobable and the probability of ( X ) is ( 5 / 12 ) and the probability of ( X ) taking place when A has happened is 3/8 while it is ( 1 / 4 ) when ( mathrm{B} ) has taken place, then
the probability of ( X ) taking place on conjunction with ( mathrm{C} ) is
A . ( 5 / 8 )
в. ( 3 / 8 )
( c cdot 5 / 24 )
D. none of these
12
1148Find the number of triangles whose vertices are at the vertices of an
octagon but none of whose sides happen to come from the octagon.
12
1149Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that the first ball is black and the second is red.
12
1150In a bolt factory, machines ( A, B ) and ( C )
manufacture ( 25 %, 35 % ) and ( 40 % )
respectively of the total number of bolts.
The percentage of defective bolts
among the manufactured bolts is ( 5 % )
for ( A, 4 % ) for ( B ) and ( 2 % ) for ( C . ) A bolt is
drawn randomly from the manufactured
products and is found to be defective then
This question has multiple correct options
A. the probability that the selected bolt is defective ( = ) 0.0345
B. the probability that the defective bolt was manufactured by machine ( A=frac{25}{69} )
C. the probability that the defective bolt was manufactured by machine ( B=frac{28}{69} )
D. the probability that the defective bolt was manufactured by machine ( C=frac{16}{69} )
12
1151The mean weight of 500 male students in a certain college is 151 pounds and the standard deviation is 15 pounds. Assuming the weights are normally distributed, find the approximate number of students weighing.
(i) between 120 and 155 pounds,
[
begin{array}{llll}
z & 0.2667 & 2.067 & 2.2667 \
& & & \
text { Area } & 0.1026 & 0.4803 & 0.4881
end{array}
]
(ii) more than 185 pounds.
12
1152In a hostel, ( 60 % ) of the students read
Hindi newspaper, ( 40 % ) read English
newspaper and ( 20 % ) read both Hindi and English newspapers. A student is selected at random. Find the probability that she reads neither Hindi nor English
newspapers.
A ( cdot frac{1}{5} )
B. ( frac{2}{5} )
( c cdot frac{3}{5} )
D. ( frac{4}{5} )
12
1153A pack of cards is counted with face downwards. It is found that one card is
missing, One card is drawn and is found
to be red. Find the probability that the missing card is red.
12
115412.
The po
The probability of India winning a test match against west
Indies is 1/2. Assuming independence from match to match
the probability that in a 5 match series India’s second win
occurs at third test is
(1995S)
(a) 1/8 (6) 1/4 (c) 1/2 (d) 213
12
1155A pair of fair dice is thrown independently three times. The probability of getting a score of exactly
9 twice is-
A ( cdot frac{1}{729} )
в. ( frac{8}{9} )
c. ( frac{8}{729} )
D. ( frac{8}{243} )
12
1156When a die is thrown, list the outcomes
of an event of getting
a) A prime number
b) A number greater than 6
12
1157In a World Cup final match against Srilanka, for six times Sachin Tendulkar
hits a six out of 30 balls he plays. What is the probability that in a given throw the ball does not hit a six?
A ( cdot frac{1}{4} )
B.
( c cdot frac{4}{5} )
D. ( frac{3}{4} )
12
1158Probability of getting a prime (or) composite is
A. Mutually exclusive
B. Likely
c. 0
D. None
12
1159Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random
from the box, find the probability that the number on the drawn card is
(i) an odd number
(ii) a perfect square
number
(iii) divisible by 5
(iv) a prime number less than 20
12
1160A letter is known to have come either
from ( L O N D O N ) or ( C L I F T O N ; ) on the
postmark only the two consecutive letters ( boldsymbol{O} boldsymbol{N} ) are ellegible. The probability that it came from ( L O N D O N ) is
A ( cdot frac{5}{17} )
в. ( frac{12}{17} )
c. ( frac{17}{30} )
D. ( frac{3}{5} )
12
11612K coins (K is an integer) each with probability P(O
( ^{A} cdot frac{K}{2 K+1} )
в. ( frac{K+1}{2 K} )
c. ( frac{K+1}{2 K+1} )
D. ( frac{2 K}{K+1} )
12
1162If ( A ) and ( B ) are mutually exclusive such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} )
find
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
1163Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket?12
1164Three of the six vertices of regular hexagon are chosen at random. The
probability that the triangle with these vertices is equilateral, equals
A. ( 1 / 2 )
в. ( 1 / 5 )
c. ( 1 / 10 )
D. ( 1 / 20 )
12
1165In an entrance test, there are multiple
choice questions. There are four possible options of which one is correct. The probability that a student knows
the answer to a question is ( 90 % ). If he
gets the correct answer to a question, then the probability that he was guessing is
A ( cdot frac{1}{37} )
B. ( frac{36}{37} )
( c cdot frac{1}{4} )
D. ( frac{1}{49} )
12
1166For any two independent events ( boldsymbol{E}_{1} ) and
( boldsymbol{E}_{2}, boldsymbol{P}left{left(boldsymbol{E}_{1} cup boldsymbol{E}_{2}right) cap(overline{boldsymbol{E}_{1}}) cap(overline{boldsymbol{E}_{2}})right} ) is
( A cdot leq frac{1}{4} )
B. ( >frac{1}{4} )
( c cdot geq frac{1}{2} )
D. None of these
12
1167Q Type your question
in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as
below :
No. of faulty packet Number of
packets
0
1
2
3
4
Total number of packets 500
If one packet is drawn from the box, what
is the probability that all the four devices in the packet are without any fault?
A . 0.5
B. 0.6
c. 0.8
D. 0.9
12
1168Given two independence events ( A ) and ( B ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( P(B / A) )
12
1169A screw factory has two machines, the
M1, which is old, and does ( 75 % ) of all the
screws, and the M2, newer but small,
that does ( 25 % ) of the screws. The ( mathrm{M} )
does ( 4 % ) of defective screws, while the
M2 just does ( 2 % ) of defective screws. If we choose a screw at random: what is
the probability that it turns out to be
defective?
A. 0.035
в. 0.045
c. 0.015
D. None of these
12
1170For two events, ( A ) and ( B ), it is given that ( boldsymbol{P}(boldsymbol{A})=frac{mathbf{3}}{mathbf{5}}, boldsymbol{P}(boldsymbol{B})=frac{mathbf{3}}{mathbf{1 0}} ) and ( boldsymbol{P}(boldsymbol{A} mid boldsymbol{B})= )
( mathbf{2} )
( frac{2}{3} . ) If ( bar{A} ) and ( bar{B} ) are the complementary
events of ( A ) and ( B ), then what is ( P(bar{A} mid bar{B}) )
equal to?
( A cdot frac{3}{7} )
B. ( frac{3}{4} )
( c cdot frac{1}{3} )
D.
12
1171In a class of 55 students, the number of
students studying in different subject are, 23 in Mathematics, 24 in physics,
19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry
and 4 in all the three subjects. Find the number of students who have taken
exactly one subject.
12
1172A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a
student will get 4 or more correct answers just by guessing is
A ( cdot frac{13}{3^{5}} )
в. ( frac{11}{3^{5}} )
c. ( frac{10}{3^{5}} )
D. ( frac{17}{3^{5}} )
12
1173The probability of getting the rotten egg from a lot of 400 eggs is ( 0.035 . ) Find the
number of rotten eggs in the lot.
12
1174If the probability of ( x ) to fail in the
examination is 0.3 and that for ( Y ) is 0.2
then the probability that either ( boldsymbol{X} ) or ( boldsymbol{Y} ) fail in the examination is
A . 0.5
B. 0.44
( c .0 .6 )
D. None of these
12
1175In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good
in all three subjects. What is the number of students who are good in either Hindi or Mathematics but not in
English?
A . 99
в. 107
c. 125
D. 130
12
1176A die is tossed twice. Getting an odd number is termed a success. The
probability distribution of number of successes ( (X) ) is formed. Then its mean,
variance are
A ( cdot 1, frac{1}{2} )
B. ( frac{1}{2}, 1 )
c. ( frac{1}{2}, frac{1}{2} )
D. 1,1
12
1177Which of the following is/are true?
A. Profitability Index (PI) is a variation of the NPV rule
B. Even in case of mutually exclusive projects a conflict of ranking will not arise between PI and NPV
C. A project should be accepted when both PI and NPV are positive
D. All of the above
E. Both (A) and
(C) above
12
1178Three balanced coins are tossed
simultaneously. If ( X ) denotes the
number of heads, find probability
distribution of ( boldsymbol{X} )
12
1179The probability of an impossible event
is
( mathbf{A} cdot mathbf{3} )
B.
c. 1
( D )
12
1180We draw two cards from a deck of
shuffled cards without replacement. Find the probability of getting the second card a queen.
A ( cdot frac{1}{13} )
в. ( frac{2}{13} )
( c cdot frac{5}{13} )
D. None of these
12
1181A bag contains some white and some black balls, all combinations of balls
being equally likely. The total number of
balls in the bag is ( 10 . ) If three balls are drawn at random without replacement and all of them are found to be black,
the probability that the bag contains 1
white and 9 black balls is
A ( cdot frac{14}{55} )
B. ( frac{12}{55} )
( c cdot frac{2}{55} )
D. ( frac{8}{55} )
12
1182There are 5 cards in a box with numbers
1 to5 written on them. If 2 cards are
picked out from the box, write all the possible outcomes and find the probpossible ability of getting both even numbers.
12
11833.
In a throw of a dice, the probability of getting an even
number is the same as that of getting an odd number.
11
1184( A=x / x ) is a two digit number, which
divisible by ( 2(text { or }) 3 ) and ( x leq 50, B= )
( x / x ) is a two digit number, which
divisible by 6 and ( x leq 50 ).Find ( n(A cup B)=? )
( n(A cap B)=? )
12
1185If head means one and tail means two
then coefficients of quadratic equation
( a x^{2}+b x+c=0 ) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A ( cdot frac{5}{8} )
B. ( frac{3}{8} )
( c cdot frac{7}{8} )
D.
12
1186Three six-faced fair dice are thrown
together let ( P(k) ) denote the probability
that the sum of the numbers appearing
on the dice is ( k(9 leq k leq 4) ). Find 54 s where ( boldsymbol{S}=sum_{boldsymbol{k}=mathbf{9}}^{mathbf{1 4}} boldsymbol{P}(boldsymbol{k}) )
12
1187The probability that a student will pass
the final examination in both English and Hindi is 0.5 and the probability of passing neither is ( 0.1 . ) If the probability of passing the English examination is ( 0.75, ) what is the probability of passing the Hindi examination?
12
1188The term law of total probability is sometimes taken to mean the
A. Law of total expectation
B. Law of alternatives
c. Law of variance
D. None of these
12
1189An electronic machine chooses random numbers from I to
30. What is the probability that the number chosen is an
even number?
(a) 15/30
(b) 1/10
(c) 1/6
(d) 1/2
11
1190If ( X ) follows a binomial distribution
with parameters ( n=8 ) and ( p=frac{1}{2}, ) then
( boldsymbol{P}(|boldsymbol{X}-mathbf{4}| leq mathbf{2}) ) is
A ( cdot frac{119}{128} )
в. ( frac{119}{228} )
c. ( frac{19}{128} )
D. ( frac{18}{28} )
12
1191One ticket is selected randomly from the set of 100 tickets numbered as
( {00,01,02,03,04,05, ldots, 98,99} . E_{1} ) and
( E_{2} ) denote the sum and product of the digits of the number of the selected ticket. The value of ( boldsymbol{P}left(frac{boldsymbol{E}_{1}=boldsymbol{9}}{boldsymbol{E}_{2}=mathbf{0}}right) ) is
A ( cdot frac{1}{19} )
B. ( frac{2}{19} )
( c cdot frac{3}{19} )
D. ( frac{1}{18} )
12
1192Three different coins are tossed
together find the probability of
i) Exactly two heads
ii) At least
one tails
ii) Almost two heads
iv) At most
two tails
v) At least two tails
vi) At most
one head
vii) At least one head
12
1193An insurance company issued 3000 scooters, 4000 cars and 5000 trucks.
The probabilities of the accident involving a scooter, a car and a truck are 0.02,0.03 and 0.04 respectively. One of the insured vehicles meet with an
accident. Find the probability that it is a
(i) scooter
(ii) car (iii) truck.
12
1194An unbiased coin is tossed. if the result
is a head, a pair of unbiased dice is rolled & the number obtained by adding the numbers on the two faces is noted. If
the result is a tail, a card from a well
shuffled pack of eleven cards numbered ( 2,3,4, dots, 12 ) is picked ( & ) the number on the card is noted. What is the
probability that the noted number is
either 7 or ( 8 ? )
A. 0.24
в. 0.27
( c .0 .3 )
D. 0.31
12
1195The probability distribution of a
discrete random variable ( X ) is:
[
boldsymbol{X}=boldsymbol{x} quad mathbf{1} quad boldsymbol{2} quad boldsymbol{3}
]
( P(X= )
( x) )
[
3 k
]
( 4 k ) ( k quad 2 k )
[
text { Find } P(X leq 4)
]
( mathbf{A} cdot frac{2}{3} )
B. ( frac{3}{4} )
( c cdot frac{4}{5} )
D. ( frac{5}{6} )
12
1196If ( A ) and ( B ) are two mutually exclusive
events, then
This question has multiple correct options
( mathbf{A} cdot P(A) leq P(bar{B}) )
B ( . P(bar{A} cap bar{B})=P(bar{A})-P(B) )
( mathbf{c} cdot P(bar{A} cup bar{B})=0 )
D . ( P(bar{A} cap B)=P(B) )
12
1197Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line ( boldsymbol{X}=boldsymbol{mu} ) (Mean)
(ii) Mean ( = ) Median ( = ) Mode
(iii) Unimodal
(iv) Points of inflexion are at ( boldsymbol{X}=boldsymbol{mu} pm boldsymbol{sigma} )
A . (i), (ii)
B. (ii), (iv)
c. (i), (ii), (iii)
D. All of these
12
1198Three cards are drawn at random
(without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence find the mean of the
distribution.
12
119930.
sum as well as
Iftwo different numbers are taken from the set (0.1
…….., 10), then the probability that their sum as we
absolute difference are both multiple of 4, is :
[JEE M 2017
(b)
ante A Band C
11
1200If the papers of 4 students can be
checked by any one of the seven teachers, then the probability that all the four papers are checked by exactly two teachers is
A ( cdot frac{6}{49} )
B. ( frac{2}{7} )
c. ( frac{32}{343} )
D. ( frac{2}{343} )
12
1201In a factory machine ( boldsymbol{A} ) produce ( mathbf{3 0 %} ) of the total output, machine ( B ) produced
( 25 % ) and the machine ( C ) produced the remaining output. If defective items produced by machine ( A, B ) and ( C ) are ( 1 %, 1.2 %, 2 % ) respectively. Three machine working together produced
10000 item in a day. An item is drawn at random from a day’s output and found to be defective.
Find the probability that it was produced by machine ( boldsymbol{B} ) ?
12
1202A bag contains 6 black and 8 white
balls. One ball is drawn at random. What
is the probability that the ball drawn is
white?
A ( cdot frac{3}{4} )
B. ( frac{4}{7} )
( c cdot frac{1}{8} )
D.
12
1203In a particular section of class ( 1 X, 40 ) students were asked about the month
of their birth and following graph was prepared for data so obtained:

Find the probability that a student of
the class was born in August.

12
1204A dice is thrown twice. A success is an
even number on each throw. Find the
probability distribution of the number
of successes.
12
1205For 3 events ( A, B ) and ( C, P( ) exactly one of the events ( A text { or } B text { occurs })=P( ) exactly one of the events ( mathrm{B} text { or } mathrm{C} text { occurs })=mathrm{P}( ) exactly one of the events ( C text { or } A text { occurs })=p & P ) (all the three events occurs
simultaneously) ( =p^{2} . ) Where ( o<p<frac{1}{2} )
then the probability of at lest one of
three events, ( A, B & C ) occurring is
A ( cdot frac{3 p+2 p^{2}}{2} )
B. ( frac{p+2 p^{2}}{2} )
c. ( frac{3 p+p^{2}}{2} )
D. ( frac{3 p+2 p^{2}}{4} )
12
1206Let ( A ) and ( B ) be two events such that
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=boldsymbol{P}(boldsymbol{A})+boldsymbol{P}(boldsymbol{B})- )
( boldsymbol{P}(boldsymbol{A}) boldsymbol{P}(boldsymbol{B}) . ) If ( boldsymbol{0}<boldsymbol{P}(boldsymbol{A})<1 ) and ( boldsymbol{0}< )
( boldsymbol{P}(boldsymbol{B})<1, ) then ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})^{prime} ) is equal to
A ( cdot 1-P(A) )
B . ( 1-Pleft(A^{prime}right) )
c. ( 1-P(A) P(B) )
D cdot ( [1-P(A)] Pleft(B^{prime}right) )
( E )
12
120713. Three of the six vertices of a regular hexagon are chosen at
random. The probability that the triangle with three vertices
is equilateral, equals
(1995S)
(a) 1/2 (b) 1/5 – (c) 1/10 (d) 1/20
11
1208In a factory which manufactures bolts, machines ( A, B ) and ( C ) manufacture ( 30 %, 50 % ) and ( 20 % ) of the bolts
respectively. Of their output ( 3 %, 4 % ) and ( 1 % ) respectively are defective bolts. bolt is drawn at random from the
product and is found to be defective Find the probability that this is not manufactured by machine B.
12
1209A player throws 2 ordinary die with faces numbered 1 to 6. What is the
probability of obtaining a total score of atmost ( 6 ? )
A ( cdot 12 / 36 )
B. ( 16 / 36 )
c. ( 15 / 36 )
D. ( 10 / 36 )
12
1210The probability of happening of an event is ( 45 % . ) The probability of an event is :
A . 45
B. 4.
( c cdot 0.45 )
D. 0.045
12
1211A bag contains 3 red and 3 green balls
and a person draws out 3 at random. He then drops 3 blue balls into the bag and again draws out 3 at random. The chance that the 3 later balls being all of different colors is
A . ( 15 % )
B . 20%
c. ( 60 % )
D. 40%
12
1212The probability that in a group of ( N )
people at least two will have the same birthday is
A ( cdot_{1-frac{(365) !}{(365)^{N}(365-N) !}} )
В ( cdot_{1+frac{(365) !}{(365)^{N}(365-N) !}} )
c. ( _{1-} frac{(365) !}{(365)^{N}(365+N) !} )
D. None of these
12
1213If ( A ) and ( B ) are any two events such that ( P(A)=frac{2}{5} ) and ( P(A cap B)=frac{3}{20}, ) then
the condition probability, ( boldsymbol{P}left(boldsymbol{A} mid boldsymbol{A}^{prime} cupright. )
( left.B^{prime}right) ), where ( A^{prime} ) denotes the complement
of ( A, ) is equal to:
A ( cdot frac{5}{17} )
в. ( frac{11}{20} )
( c cdot frac{1}{4} )
D. ( frac{8}{17} )
12
1214A seven digit number is formed by using 0,1,2,3,4,8,9 without repetition. Then the probability that it is divisible by 4 is
A ( cdot frac{53 times 4 !}{5 times 6 !} ! )
в. ( frac{53}{180} )
c. ( frac{53}{6 times 6 !} )
D. None of these
12
1215Obtain the probability distribution of
the number of sixes in two tosses of a
fair die
12
1216If ( P(1) ) be the probability of an event ( A )
then
A. ( -1 leq P(1) leq 1 )
B. ( 0 leq P(1)<0.5 )
c. ( 0 leq P(1) leq 1 )
D. None of these
12
1217Die ( A ) has 4 red and 2 white faces where
as die ( B ) has two red and 4 white faces.
( A ) fair coin is tossed. If head turns up,
the game continues by throwing die ( A )
if tail turns up then die ( B ) is to be used. If the first two throws resulted in
red, what is the probability of getting red face at the third throw?
( A cdot frac{2}{5} )
B. ( frac{1}{5} )
( c cdot frac{3}{5} )
D. ( frac{1}{2} )
12
1218The probability that, on the examination
day, the student ( S_{1} ) gets the previously
allotted seat ( R_{1} ) and NONE of the
remaining students gets the seat previously allotted to him/her is?
( A cdot frac{3}{40} )
B. ( frac{1}{8} )
c. ( frac{7}{40} )
D. ( frac{1}{5} )
12
1219When two dice are thrown, list the number outcomes of an even of getting
equal to 8
A .2
B. 3
( c cdot 4 )
D. 5
12
1220In a survey of 600 students in a school,
(i) 160 students were found to be taking
Tea 215 taking Coffee, 150 were taking both Tea and Coffee.
(ii) 150 students were found to be
taking tea and 225 taking coffee, 100 were taking both Tea and Coffee. Find how many students were taking neither tea nor coffee?
12
1221Not more than one fuses.12
1222The act of throwing a die is called an
A . outcomes
B. event
c. experiment
D. sample
12
1223Given two independence events ( A ) and
( B, ) such that ( P(A)=0.3 ) and ( P(B)= )
0.6. Find ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
12
1224A bag contains ( n+1 ) coins. It is known that one of these coins has heads on
both sides, whereas the other coins are fair. One coin is selected at random and
tossed. If the probability that the toss results in heads is ( 7 / 12, ) find ( n )
12
1225Two dice are thrown The events ( A, B )
and ( C ) are as follows:
A : getting an even number on the first die
B : getting an odd number on the first die
C : getting the sum of the numbers on the dice ( leq 5 )
Describe the events
(i) ( A^{prime} )
(ii) not ( boldsymbol{B} )
(iii) ( boldsymbol{A} ) or ( boldsymbol{B} )
(iv) ( A ) and ( B )
(v) ( A ) but not ( C )
(vi) ( B ) or ( C )
(vii) ( B ) and ( C )
(viii) ( boldsymbol{A} cap boldsymbol{B}^{prime} cap boldsymbol{C}^{prime} )
12
1226The probability distribution of a random variable ( X ) is given below:
[
begin{array}{lllll}
mathrm{x}: & 0 & 1 & 2 & 3 \
mathrm{P}(mathrm{x}): & mathrm{k} & frac{k}{2} & frac{k}{4} & frac{k}{8}
end{array}
]
Determine the value of ( X, ) if ( k=frac{8}{X} )
12
1227How many different numbers, greater
than 50000 can be formed with the
( operatorname{digits} mathbf{0}, mathbf{1}, mathbf{1}, mathbf{5}, mathbf{9} )
12
1228DIA 2
SUP
6.
It is known that a box of 600 electric bulbs contains 12
defective bulbs. One bulb is taken out at random from this
box. What is the probability that it is a non-defective bulb?
11
1229( A ) and ( B ) are two independent events. The probability that both ( A ) and ( B ) occur is ( frac{1}{6} )
and the probability that neither of them occurs is ( frac{1}{3} . ) The probability of
occurrence of A is?
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{5}{6} )
D.
12
1230A lot of contains 20 articles. The
probability that the lot contains exactly
2 defective articles is 0.4 and the
probability that the lot contains exactly 3 defective articles is ( 0.6 . ) Articles are
drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is
the probability that the testing procedure ends at the twelfth testing?
A ( cdot frac{99}{1900} )
в. ( frac{99}{950} )
c. ( frac{198}{1900} )
D. ( frac{99}{1000} )
12
1231Two events ( A ) and ( B ) are such that
( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} )
( boldsymbol{B})=mathbf{0 . 5 . F i n d} boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
( mathbf{A} cdot mathbf{0} )
B. 0.2
( c .0 .3 )
D. 0.5
12
1232Two numbers are selected at random
(without replacement) the first six
positive integers. Let ( X ) denote the
larger of the two numbers obtained.
Find ( boldsymbol{E}(boldsymbol{X}) )
12
1233If it rains on Republic Day parade an
Auto Riksha earns Rs. ( 240, ) on the other
hand it does not rain he loses Rs. ( 60 . ) The
probability of rain on Republic Day parade is ( 0.6 . ) What is the value of expected income of an Auto Riksha on
Republic Day parade?
A . Rs. 150
B. Rs. 45
c. Rs. 120
D. Rs. 10
12
1234( A ) can hit target three times in six
shots, ( B ) can hit target 2 times in six
shots and ( C ) can hit target 4 times in a
6 shots. They fix a ball. But what is the probability that they hit ball in atleast two shots.
12
1235The probability that ( A ) hit a target is
( 1 / 4 ) and the probability that ( B ) hits the target is ( 1 / 3 . ) If each of them fired once, what is the probability that the target will be hit atleast once?
12
1236There are 3 men and 2 women. a
‘Gramswachhatta Abhiyan’ committee of two is to be formed:
( P ) is event that the committee should
contain at least one woman.
( Q ) is event that the committee should
contain one man and one women.
( R ) is the event there should not be a
women in the committee.
( S ) is the sample space.
Which of the following options is
correct?
A ( . n(S)=10, n(P)=7, n(Q)=1, n(R)=3 )
В. ( n(S)=10, n(P)=7, n(Q)=3, n(R)=3 )
c. ( n(S)=10, n(P)=7, n(Q)=2, n(R)=3 )
D. ( n(S)=10, n(P)=7, n(Q)=6, n(R)=3 )
12
1237In a hockey match, both teams ( A ) and ( B )
scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team ( A ) was
asked to start, find their respective probabilities of winning the match and state whether the decision of the referee
was fair or not.
12
1238Two coins are tossed simultaneously.
Write the sample space ( S ) and the
number of sample point ( n(S) . A ) is the
event of getting at least one head. Write
the event ( A ) in set notation and find
( boldsymbol{n}(boldsymbol{A}) )
12
1239The probability mass function (p.m.f) of
( X ) is given below:
[
begin{array}{lllll}
X=x & 1 & 2 & 3 \
P(X=x) & frac{1}{5} & frac{2}{5} & frac{2}{5}
end{array}
]
12
1240If ( boldsymbol{E} ) and ( boldsymbol{F} ) are independent events such
that ( boldsymbol{P}(boldsymbol{E})=mathbf{0 . 7} ) and ( boldsymbol{P}(boldsymbol{F})=mathbf{0 . 3}, ) then ( mathrm{P} )
( (boldsymbol{E} cap boldsymbol{F}) )
A . 0.4
B.
c. 0.21
D. None
12
1241Addition Theorem of Probability states
that for any two events ( A ) and ( B )
( mathbf{A} cdot P(A cup B)=P(A)+P(B) )
B ( cdot P(A cup B)=P(A)+P(B)+P(A cap B) )
( mathbf{c} cdot P(A cup B)=P(A)+P(B)-P(A cap B) )
D ( . P(A cup B)=P(A) times P(B) )
12
12426.
For any
For any two events A and B in a sample space
(1991,- 2 Marks)
(a) P(A/B) P(A)+PB)- P(B) +0 is always true
P(B)
(b) P(
AB) = P(A) – P(AB) does not hold
© P(AUB) = 1- P(Ā) P(B), if A and B are independent
(d) P(AUB) = 1- PĀ) P(B), if A and B are disjoint.
12
1243If ( A, B ) are two events with ( P(A cup B)= )
( mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 1 5}, ) then find the
value of ( boldsymbol{P}left(boldsymbol{A}^{C}right)+boldsymbol{P}left(boldsymbol{B}^{C}right) )
12
1244If ( A ) and ( B ) are mutually exclusive such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} )
find
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}) )
12
1245Statement 1: The variance of first n even
natural numbers is ( frac{mathbf{n}^{2}-mathbf{1}}{mathbf{4}} )
Statement 2: The sum of first n natural
numbers is ( frac{mathbf{n}(mathbf{n}+mathbf{1})}{mathbf{2}} ) and the sum of
squares of first n natural numbers is ( frac{mathbf{n}(mathbf{n}+mathbf{1})(mathbf{2 n}+mathbf{1})}{mathbf{6}} )
A. Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1
c. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true
12
124611. A randem variable thans Poisson distribution with mean>
A random variable X has Poisson distribution with mean 2.
Then P(X>1.5) equals
[2005]
(b) 0
12
124714.
Two aeroplanes I and II
probabilities of I and
respectively. The
aeroplanes I and II bomb a target in succession. The
habilities of I and Il scoring a hit correctly are 0.3 and 0.2
ectively. The second plane will bomb only if the first
misses the target. The probability that the target
the second plane is
[2007]
(a) 0.2 (b) 0.7 (c) 0.06 (d) 0.14
cs :
12
1248An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top card is a black card.
12
124928. Three randomly chosen non-negative integers x, y and z
are found to satisfy the equation x + y + z = 10. Then the
probability that z is even, is
36
(a)
(d)
11
1250An unbiased normal coin is tossed ( n )
times. Let ( E_{1}: ) event that both heads and
tails are present in ( n ) tosses. ( E_{2} ) :event that the coin shows up heads at most
once. The value of ( n ) for which ( E_{1} ) and ( E_{2} )
are independent is
( A )
B. 2
( c cdot 3 )
D. 4
12
1251Which of the following is not the outcome while Spinning a wheel
( A )
B. B
( c cdot c )
( D )
12
1252A card is drawn at random from a pack
of 52 cards. Find the probability that the card drawn is a jack, a queen or a king.
12
1253Three coins are tossed simultaneously:
( P ) is the event of getting at least two
heads.
( Q ) is the event of getting no heads.
( R ) is the event of getting heads on second coin. Which of the following pairs is mutually exclusive?
This question has multiple correct options
A. ( Q, R )
в. ( Q, P )
c. ( P, R )
D. None of these
12
1254If ( Pleft(E_{k}right) propto k ) for ( 0 leq k leq n, ) then the
probability that ( X ) is the only student to pass the examination is
A ( cdot frac{3}{n(n+1)} )
в. ( frac{6}{n(n+1)(2 n+1)} )
( c cdot frac{1}{n} )
D. ( frac{1}{n(2 n+1)} )
12
1255The numbers 1,2,3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other without replacement. Describe the following events: ( A= ) The number on the first slip
is larger than the one on the second slip. ( B= ) The number on the second slip is greater than ( 2 quad C= ) The sum of the numbers on the two slip is 6 or 7 ( D= ) The number on the second slips is twice that on the first slip. Which pair
(s) of events is (are) mutually exclusive
12
1256If ( mathrm{S} ) is the sample space for the event ( mathrm{A} )
then find the correct alternative from
the following:
A ( .0 geq P(A) geq 1 )
B. ( 0 leq P(A)<1 )
c. ( 0<P(A) leq 1 )
D. ( 0 leq P(A) leq 1 )
12
1257Difference between sample space and
subset of sample space is considered
as
A. numerical complementary events.
B. equal compulsory events
c. complementary events.
D. compulsory events
12
1258In a sample survey of 640 people, it was found that 400 people have a secondary school certificate. If a person is selected at random, what is the probability that the person does not have such
certificate?
( mathbf{A} cdot 0.375 )
B. 0.625
c. 0.725
D. 0.875
12
1259The given graph represent the how much consumers would be willing to
pay for store brand and brand name
products. If a consumer is chosen at
random, then the probability that the
consumer is will to pay at least ( $ 8 ) for
the product is ( frac{u}{b}, ) where ( a, b ) are ( c 0 )
primes. Find the value of ( b-a ? )

Store Brand ( square ) Brand Name

12
1260The random variable ( x ) follows normal
distribution
Then the value of ( C ) is
A ( cdot sqrt{2 pi} )
в. ( frac{1}{sqrt{2 pi}} )
c. ( 5 sqrt{2 pi} )
D. ( frac{1}{5 sqrt{2 pi}} )
12
1261In the year 2009 , during rainy season of 90 days, it was observed that it rain to
20 days only. Find the probability that it did not rain.
12
12626 married couples are standing in a
room. If 4 people are chosen at random, then the chance that exactly one
married couple is among the 4 is?
A ( cdot frac{16}{33} )
в. ( frac{8}{33} )
c. ( frac{17}{33} )
D. ( frac{24}{33} )
12
1263If ( A, B ) and ( C ) are mutually exclusive and exclusive events of a random
experiment such that ( boldsymbol{P}(boldsymbol{B})=frac{boldsymbol{3}}{2} boldsymbol{P}(boldsymbol{A}) )
and ( P(C)=frac{1}{2} P(B), ) then ( P(A cup C)= )
A ( cdot frac{10}{13} )
в. ( frac{3}{13} )
c. ( frac{6}{13} )
D. ( frac{7}{13} )
12
1264A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number ( 1,2,3, dots dots ., 12 ) as shown in figure. What is the probability that it will point to multiple of ( 4 ? )
( A cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{4} )
D.
E. None of these
12
1265A die is thrown, write a sample space
( (S) ) and ( n(S) . ) If event ( A ) is getting a number greater than ( 4, ) write event ( A ) and ( n(A) )
12
1266A man alternatively tosses a coin and throws a die. The probability of getting a head on the coin before he gets 4 on the
die is
A ( cdot frac{6}{7} )
в. ( frac{2}{3} )
( c cdot frac{3}{4} )
D.
12
1267If two events ( A ) and ( B ) such that
( boldsymbol{P}left(boldsymbol{A}^{prime}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} ) and ( boldsymbol{P}(boldsymbol{A} cap )
( B)=0.3, ) then ( Pleft(B mid A cup B^{prime}right) ) is
A . ( 3 / 8 )
B. 2 /
c. ( 5 / 6 )
D. ( 1 / 4 )
12
1268From 7 gentlemen and 4 ladies, a
committee of 5 is to be formed. The
probability that this can be one so as to include at least one lady is
A ( cdot frac{^{7} C_{5}}{^{11} C_{5}} )
в. ( frac{4}{^{11} C_{5}} )
( ^{mathbf{C}} cdot_{1-frac{^{7} C_{5}}{11} C_{5}} )
D. ( _{1-frac{4}{11} C_{5}} )
12
1269In a simultaneous throw of a pair of
dice, if the probability of getting a total of 9 or 11 is ( frac{1}{x} . ) Find ( x )
12
1270If ( C ) and ( D ) are two events such that
( C subset D ) and ( P(D) neq 0, ) then the correct
statement among the following is
( mathbf{A} cdot P(C mid D)<P(C) )
( ^{mathbf{B}} P(C mid D)=frac{P(D)}{P(C)} )
c. ( P(C mid D)=P(C) )
D. ( P(C mid D) geq P(C) )
12
1271A man is known to speak the truth 3 out of 4 times. He throws a die and reports
that it is a six. The probability that it is actually a six is
A ( cdot frac{3}{8} )
B. ( frac{1}{5} )
( c cdot frac{3}{4} )
D. None of these
12
1272An urn contains 6 white and 4 black
balls. A fair die whose faces are
numbered from 1 to 6 is rolled and
number of balls equal to that of the number appearing on the die is drawn from the urn at random. The probability that all those are white is
A. 1 5
B. ( frac{2}{5} )
( c cdot frac{3}{5} )
( D cdot frac{4}{5} )
12
1273A fair die is rolled 180 times. The
expected number of 6 is
A . 50
B. 30
c. 10
D.
12
1274Three bags contain 2 silver, 5 copper coins, and 3 silver, 4 copper coins and 5 silver, 2 copper coins respectively. A bag
is chosen at random and a coin is
drawn from it which happens to be silver. What is the probability that it has come from third bag?
12
1275The mean score of 1000 students for an
examination is 34 and standard
deviation is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) Determine the limits of the marks of
the central ( 70 % ) of the candidates
( {P[0<z<0.25]=0.0987 ; P[0<z< )
1.63 ( ]=mathbf{0 . 4 4 8 4} ; P[mathbf{0}<boldsymbol{z}<mathbf{1 . 0 4}]= )
( mathbf{0 . 3 5}} )
12
1276In a class ( 5 % ) of boys and ( 10 % ) of girls have an I.Q of more than ( 150 . ) In this class
( 60 % ) of students are boys. If a student is
selected at random and found to have
an I.Q. of more than ( 150 . ) Find the probability that the student is a boy.
A ( cdot frac{3}{7} )
B. ( frac{23}{7} )
( c cdot frac{3}{5} )
D. None of these
12
1277A discrete random variable ( X, ) can take
all possible integer values from 1 to ( K )
each with a probability ( 1 / K . ) Its mean is
( mathbf{A} cdot K )
в. ( K+1 )
c. ( K / 2 )
D. ( K / 4 )
12
1278For any two events ( A ) and ( B ) in a sample
space:
This question has multiple correct options
( ^{mathbf{A}} cdot p(A / B) geq frac{P(A) P(B)-1}{P(B)} P(B) neq 0 ) is always true
B ( cdot P(A cap bar{B})=P(A)-P(A cap B) ), does not hold
( mathbf{c} cdot P(A cup B)=1-P(bar{A}) P(bar{B}), ) if ( A ) and ( B ) are independent
D ( cdot P(A cup B)=1=P(bar{A}) P(bar{B}) ), if ( A ) and ( B ) are disjoint.
12
1279Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of
introducing a new product is 0.7 and
the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
12
1280If ( A, B, C ) are three independent events
of an experiment such that, ( boldsymbol{P}(boldsymbol{A} cap ) ( left.boldsymbol{B}^{C} cap boldsymbol{C}^{C}right)=frac{1}{4}, boldsymbol{P}left(boldsymbol{A}^{C} cap boldsymbol{B} cap boldsymbol{C}^{C}right)= )
( frac{1}{8}, Pleft(A^{C} cap B^{C} cap C^{C}right)=frac{1}{4}, ) then find
( boldsymbol{P}(boldsymbol{A}), boldsymbol{P}(boldsymbol{B}), boldsymbol{P}(boldsymbol{C}) )
12
1281An event in which all the possible outcomes of the experiments are present is known as event
A. a complement.
B. an experiment
c. a sample space.
D. an exhaustive event.
12
1282Assertion
Odd in favour of an event ( A ) are ( 2: 1 & )
odd in favour of ( A cup B ) are 3: 1 then
( frac{1}{12} leq P(B) leq frac{3}{4} )
Reason
If ( boldsymbol{A} cap boldsymbol{B} subset boldsymbol{A} ) then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) leq boldsymbol{P}(boldsymbol{A}) )
A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
B. Both Assertion & Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
12
1283A bag contains 5 red balls and 8 blue
balls. It also contains 4 green and 7
black balls. If a ball is drawn at random,
then find the probability that it is not green
A ( cdot frac{5}{6} )
B. ( frac{1}{4} )
( c cdot frac{1}{6} )
D. ( frac{7}{4} )
12
1284An urn A contains 4 white and 6 redd
balls. Three balls are drawn at random the expected number of white balls drawn is
A . 3.0
B. 1.8
c. 1.2
D. 1.
12
1285Events ( boldsymbol{A} ) and ( boldsymbol{B} ) are such that ( boldsymbol{P}(boldsymbol{A})= ) ( frac{1}{2}, P(B)=frac{7}{12} ) and
( P(text { not } A text { or } operatorname{not} B)=frac{1}{4} . ) State whether
( A ) and ( B ) are independent?
A. True
B. False
12
1286A die is throw once. Find the probability
of getting
(1)an even number
(2)a number less than 5
(3)a number greater than 2
(4)a number between 3 and 6
(5)a number other than 3
(6)the number 5
12
1287Suppose that two cards are drawn at random from a deck of cards. Let ( X ) be
the number of aces obtained. Then the
value of ( boldsymbol{E}(boldsymbol{X}) ) is
A ( cdot frac{37}{221} )
в. ( frac{5}{13} )
c. ( frac{1}{13} )
D. ( frac{2}{13} )
12
1288Let ( A ) and ( B ) be two events such that
( boldsymbol{P}(overline{boldsymbol{A} cup boldsymbol{B}})=frac{1}{6}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=frac{1}{4} ) and
( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for the
complement of the event A. Then, the
events ( A ) and ( B ) are
A. Independent but not equally likely
B. Independent and equally likely
c. Mutually exclusive and independent
D. Equally likely but not independent
12
1289In a group of 400 people, 160 are
smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are ( 35 %,, 20 % )
and ( 10 % ) respectively. A person is chosen from the group at random and is
found to be suffering from the disease. What is the probability that the selected person is a smoker and non-
vegetarian?
12
1290If ( A ) and ( B ) are two events. The probability
that at most one of ( A, B ) occurs is
A ( .1-P(A cap B) )
в. ( P(bar{A})+P(bar{B})-P(bar{A} cap B) )
c. ( P(bar{A})+P(bar{B})+P(bar{A} cap bar{B}) )
D. All of the above
12
1291Four cards are drawn from a deck of 52
cards, the probability of all being spade ¡s
( ^{A} cdot frac{1}{256} )
в. ( frac{1}{56} )
c. ( frac{1}{64} )
D. ( frac{31}{256} )
12
129216. Let É and F be two independent events. The probability
that exactly one of them occurs is 11 and the probability of
25
none of them occurring is – fP(T) denotes the probability
of occurrence of the event T, then
(2011)
(@) PLE)= ,PF)=} (6) PCE) = 5, PC)=}
(C) PE)= 3, PCP)= (A) PLE)= 3, PCP)=
12
1293According to the property of probability, the probability of an event cannot be
A. greater than zero
B. equal to zero
c. less than zero
D. equal to one
12
1294If ( X ) follows a binomial distribution
with parameters ( n=8 ) and ( P=frac{1}{2}, ) than
( boldsymbol{P}(|boldsymbol{x}-mathbf{4}| leq mathbf{2})= )
A ( cdot frac{119}{128} )
в. ( frac{9}{128} )
c. ( frac{101}{128} )
D. ( frac{11}{128} )
12
1295From a lot of 15 bulbs which include 5
defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of
the distribution.
12
1296If the value of ( x ) is 6
A ( cdot frac{2}{3} )
B. ( frac{1}{3} )
( c cdot frac{5}{6} )
D.
12
1297There are two groups of subjects one of which consists of 5 science subjects and 3 engineering subjects and the
other consists of 3 science and 5
engineering subjects. An unbaised die
is cast. If number 3 or number 5 turns
up, a subject is selected at random
from the first group, other wise the
subject is selected at random from the
second group. Find the probability that an engineering subject is selected ultimately.
A ( cdot frac{13}{24} )
B. ( frac{1}{3} )
( c cdot frac{2}{3} )
D. ( frac{11}{24} )
12
1298The annual salaries of employees in a large company are approximately normally distributed with a mean of ( mathbf{5 0}, mathbf{0 0 0} ) and a standard deviation of ( 20,000 . ) What percent of people earn
between 45,000 and ( 65,000 ? )
A . ( 56.23 % ) %
B . ( 47.4 % )
c. ( 37.2 % )
D. 38.56%
12
1299A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let ( A ) be the event, ‘the
number is even’, and ( B ) be the event,’the
number is red’. Then ( A ) and ( B ) are
independent events.
A. True
B. False
12
1300The largest possible variance of a binomial variate is
A ( . n )
в. ( frac{n}{2} )
c. ( frac{n}{4} )
D. ( frac{n}{6} )
12
1301In a sequence of independent trials, the
probability of success is ( 1 / 4 . ) If ( p ) denotes the probability that the second
success occurs on the fourth trial or
later trial, find ( 32 p )
12
1302In a horse race there are 18 horses
numbered from 1 to 18. The probability that horse 1 would win is ( frac{1}{6}, ) horse 2 is ( frac{1}{10} ) and 3 is ( frac{1}{8} . ) Assuming a tie is impossible, the chance that one of the
three horses wins the race, is
A. ( frac{143}{420} )
B. ( frac{119}{120} )
C. ( frac{47}{120} )
D. ( frac{1}{5} )
12
1303Two fair dice are thrown. What is the
probability that the two scores do not
add to ( 5 ? )
( A cdot frac{7}{9} )
в. ( frac{5}{9} )
( c cdot frac{8}{9} )
D. ( frac{1}{9} )
12
1304A ball contains ( x ) white, ( y ) red, ( z ) blue
balls. A ball is drawn at the random
then, what is the probability of drawing
blue ball.
12
1305Let ( E_{1}, E_{2}, E_{3} dots E_{N} ) be the ‘n’ exhaustive
events in a random experiment then
( boldsymbol{p}left(boldsymbol{E}_{1}right) boldsymbol{p}left(, boldsymbol{E}_{2}right), boldsymbol{p}left(boldsymbol{E}_{3}right) ldots boldsymbol{p}left(boldsymbol{E}_{N}right) ) is
A. less than
B. equal to
c. greater than 1
D. none
12
1306Two balls are drawn at random with
replacement from a box containing 10
black and 8 red balls. Find the
probability that one of them is black and another is red.
12
1307There are 500 wrist watches in a box.
Out of these 50 wrist watches are found defective. One watch is drawn randomly from the box. Find the probability that wrist watch chosen is a defective watch.
12
1308The probability of getting number 10 in a throw of a dice is
A. 0
B.
( c cdot 0.5 )
D. 0.75
12
1309When two dice are rolled :
List the outcomes for the event that
total is less than 5 .
12
1310A die is thrown twice. Each time the
number appearing on it is recorded. Describe the following event:
( B= ) Both numbers are even
12
1311A medicine is known to be ( 75 % ) effective
to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is curved by this medicine?
A ( cdot frac{1}{1024} )
в. ( frac{243}{1024} )
c. ( frac{1023}{1024} )
D. ( frac{781}{1024} )
12
1312A die is thrown twice and the sum of the
numbers appearing is observed to be 6 What is the conditional probability that
the number 4 has appeared at least once?
12
1313A coin is tossed 1000 times with the
following frequencies:
Head: ( 445, ) Tail: 555
When a coin is tossed at random, what
is the probability of getting a tail?
12
1314A fair coin is tossed four times. The
probability that the tails exceed the heads in number is
( ^{mathbf{A}} cdot_{frac{4}{3} C}left(frac{1}{2}right)^{4} )
( ^{mathbf{B}} cdot_{3}^{4} Cleft(frac{1}{2}right)^{4}+left(frac{1}{2}right)^{4} )
( ^{c} cdotleft(frac{1}{2}right)^{4} )
( ^{mathrm{D}} cdot_{3}^{4} Cleft(frac{1}{3}right)^{2}left(frac{2}{3}right)^{1} )
12
1315Рогдсо о
стар, тоороо оо.
For two given events A and B, P(
A B) (1988 – 2 Marks)
(a) not less than P (A)+P (B)-1
(b) not greater than P (A)+P(B)
(c) equal to P (A) + P(B)-P (AUB)
(d) equal to P (A) + P(B) + P (AUB)
11
1316A die is thrown thrice. A success is 1 or 6
in a throw. If the sum of the mean and variance of the number of successes is ( frac{a}{3}, ) the value of a is
12
1317Red on first draw and red on second
draw
12
1318Tossing a coin is an example of
A. Infinite discrete sample space
B. Finite sample space
c. continuous sample space
D. None of these
12
1319Which one of the following is correct?
A. An event having no sample point is called an elementary event
B. An event having one sample point is called an elementary event
C. An event having two sample point is called an elementary event
D. An event having many sample point is called an elementary event
12
1320If ( x ) is a random variable with
probability distribution ( boldsymbol{p}(boldsymbol{x}=boldsymbol{k})= )
( frac{(boldsymbol{k}+mathbf{1}) boldsymbol{C}}{mathbf{2}^{k}}, boldsymbol{k}=mathbf{0}, mathbf{1}, mathbf{2}, mathbf{3}, dots dots dots dots, ) then
find ( C )
12
1321If ( A ) and ( B ) are events having probabilities, ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 6 , P}(boldsymbol{B})= )
( mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0}, ) then the probability
that neither ( A ) nor ( B ) occurs is
A ( cdot frac{1}{4} )
B. 1
( c cdot frac{1}{2} )
( D )
12
1322Rajnikant has 12 sketch pens and 8 fountain pens. He gave two of the pens
to his brother. Find the probabilities of the following events using tree diagram
i) Both the pens are sketch pens.
ii) Only one is a sketch pen
iii) Neither of them are sketch pens.
12
1323If the variance of a random variable ( X ) is
( sigma^{2}, ) then the variance of the random
variable X-5 is??
( mathbf{A} cdot 5 sigma^{2} )
B . ( 25 sigma^{2} )
( mathbf{c} cdot sigma^{2} )
D. ( 2 sigma^{2} )
12
1324A die is tossed twice. Find the
probability of getting 4,5 or 6 on the
toss and 1,2,3 or 4 on the second toss.
12
1325A bag contains 4 white, 7 black and 5
green balls. What is the probability of picking white?
12
1326A die is thrown. If ( A ) is the event that the
number on upper face is an even, then
write sample space and event ( boldsymbol{A} ) in set
notation.
12
1327Simone and her three friends were
deciding how to pick the song they will ( operatorname{sing} ) for their school’s talent show. They
decide to roll a number cube.
The person with the lowest number chooses the song. If her friends rolled a
( 6,5, ) and ( 2, ) what is the probability that Simone will get to choose the song?
A. ( frac{1}{6} )
B.
c. 0
D.
12
1328If two events ( A ) and ( B ) such that
( boldsymbol{P}left(boldsymbol{A}^{c}right)=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} cap )
( left.left.boldsymbol{B}^{c}right)=mathbf{0 . 5}, boldsymbol{P}left[boldsymbol{B} / boldsymbol{A} cup boldsymbol{B}^{c}right)right]=frac{1}{k}, ) then
value of k is
12
1329Suppose an integer from 1 through 100 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 912
1330(
102
A bag contains 4 blue, 5 red and 7 green balls. If a ball is
drawn at random, what is the probability that it is blue?
(a) 4/16
(b) 1/4
(c) 1/256
(d) 1/64
11
1331A family has two children. What is the
probability that both the children are boys given that at least one of them is a boy?
12
1332You enter a chess tournament where
your probability of winning a game is 0.3 against half the players (call them
type 1 ), 0.4 against a quarter of the players (call them type 2 ), and 0.5 against the remaining quarter of the
players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning?
A. 0.375
в. 0.986
( c cdot 0.236 )
D. 0.135
12
1333The probability that at least one of the
events ( A ) and ( B ) occurs is 0.7 and they occur simultaneously with probability
( 0.2 . ) Then ( P(bar{A})+P(bar{B})= )
A . 1.8
B. 0.6
c. ( 1 . )
D. 1.
12
1334Two cards are drawn simultaneously
from a well shuffled pack of 52 cards.
The expected number of aces is
A ( cdot frac{4}{13} )
в. ( frac{3}{13} )
c. ( frac{2}{13} )
D. ( frac{1}{13} )
12
1335The probability of event is 1
A. Sure
B. Impossible
c. exclusive
D. mutually exclusive
12
1336A bag contains 6 red, 4 white and 8 blue balls. If three ball are drawn at random,
find the probability that:
(i) All the three balls are red.
(ii) All the three balls are blue.
( A )
(i) ( frac{5}{204}, ) (ii) ( frac{7}{102} )
в.
(i) ( frac{9}{204}, ) (ii) ( frac{7}{102} )
( c )
(i) ( frac{7}{204}, ) (ii) ( frac{5}{102} )
D. None of these
12
1337( Pleft(A / B^{prime}right) ) is defined only when
( A cdot B ) is not a sure event
B. ( B ) is a sure event
c. ( B ) is an impossible event
D. ( B ) is not an impossible event
12
1338If three dice are thrown, then the
probability that they show the numbers in A.P.is
A ( cdot frac{1}{36} )
в. ( frac{1}{18} )
( c cdot frac{2}{9} )
D. ( frac{5}{18} )
12
133920.
nts.
21. Let EC denote the complement of an event E. Let E, F, G be
pairwise independent events with P(G) > 0 and
P(EnFnG)=0. Then P(ECF|G) equals (2007-3 marks)
(a) P(EC) + P(F) (b) P(EC) – P(F)
(C) P(E)- P(F) (d) P(E)- P(F)
12
1340( operatorname{Let} boldsymbol{H}_{1}, boldsymbol{H}_{2}, boldsymbol{H}_{3}, dots, boldsymbol{H}_{n} ) be mutually
exclusive and exhaustive events with
( boldsymbol{P}left(boldsymbol{H}_{i}right)>0 ; boldsymbol{i}=mathbf{1}, boldsymbol{2}, boldsymbol{3}, ldots, boldsymbol{n} . ) Let ( mathrm{E} ) be any
other event with ( 0<P(E) )
( boldsymbol{P}left(boldsymbol{E} mid boldsymbol{H}_{i}right) cdot boldsymbol{P}left(boldsymbol{H}_{i}right) ) for ( boldsymbol{i}=mathbf{1}, boldsymbol{2}, boldsymbol{3}, dots, boldsymbol{n} )
STATEMENT-2 ( sum_{i=1}^{n} Pleft(H_{i}right)=1 )
A. Statement-1 is True, Statement-2 is True; Statement – is a correct explanation for Statement- –
B. Statement-1 is True, Statement-2 is True; Statement – is Not a correct explanation for Statement- 1
c. Statement- – – is True, Statement – 2 is False
D. Statement-1 is False, Statement-2 is True
12
1341Two coins are tossed, ( A ) is the event of
getting at most one head, ( B ) is the event
getting both heads, ( C ) is the event of getting same face on both the coins. The events ( A ) and ( B ) are:
A. Mutually exhaustive
B. Mutually exclusive
c. same
D. None of these
12
1342A card is drawn from a deck of cards.
What is the probability that it is either a spade or an ace or both
A ( cdot frac{7}{13} )
в. ( frac{10}{13} )
c. ( frac{4}{13} )
D. ( frac{5}{13} )
12
1343A card from a pack of 52 cards is lost. from the remaining cards of pack, two cards are drawn and are found to be
both diamonds. Find the probability of the lost card being a diamond.
12
1344In a group of 10 children, there are 6
boys and 4 girls, 3 children are selected at random. Find the probability that the selected group have only one special girl.
12
1345One hundred identical coins, each with probability, ( p, ) of showing up heads are
tossed once. If ( 0<p<1 ) and the
probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of ( p ) is:
( A cdot frac{1}{2} )
в. ( frac{49}{101} )
c. ( frac{50}{101} )
D. ( frac{51}{101} )
12
1346The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the
remaining cards. Find the probability of getting a card of A King.
12
1347A two-digit number is formed with the
digits 2,5 and ( 7, ) where repetition of digits is not allowed. Find the probability that the number so formed
is a square number
12
1348An unbiased dice is tossed, The probability of getting a
multiple of 3 is
1.
711f
11
1349The probability that a man will be alive in 40 years is ( frac{3}{5}, ) and the probability
that his wife will also survive 40 years is ( frac{2}{3} . ) Find the probability that both will be alive
A
B. ( frac{4}{5} )
( c cdot frac{2}{15} )
D. ( frac{6}{15} )
12
1350There are n different objects, ( 1,2,3,4, ldots )
( n, ) distributed at random in n places
marked ( 1,2,3, ldots, ) n. If ( p ) is the probability that at least three of the objects occupy
places corresponding to their number, find ( 6 p )
12
1351In a group 14 males and 6 females, 8
and 3 of the males and females
respectively are aged above 40 years. The probability that a person selected at random from the group is aged above
40 years, given that the selected person is female, is
A ( cdot frac{2}{7} )
B. ( frac{1}{2} )
( c cdot frac{1}{4} )
D.
12
1352A card is thrown from a pack of 52 cards
so that each cards equally likely to be selected. In which of the following cases are the events ( A ) and ( B ) independent?
12
1353( A, B, C ) are three mutually independent
with probabilities 0.3,0.2 and 0.4 respectively. What is ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap boldsymbol{C}) ? )
A. 0.400
B. 0.240
c. 0.024
D. 0.500
12
1354In a single throw of two dice, what is the probability of
getting a total of 11.
(a) 1/9
(6) 1/18
(c) 1/12
(d) 2/36
11
1355If ( frac{1+3 p}{3}, frac{1-p}{4} ) and ( frac{1-2 p}{2} ) are mutually exclusive events. Then, range
of ( p ) is
A ( cdot frac{1}{3} leq p leq frac{1}{2} )
в. ( frac{1}{2} leq p leq frac{1}{2} )
c. ( frac{1}{3} leq p leq frac{2}{3} )
D. ( frac{1}{3} leq p leq frac{2}{5} )
12
1356Xavier, Yvonne, and Zelda each try
independently to solve a problem. If their individual probabilities for success are ( frac{1}{4}, frac{1}{2} ) and ( frac{5}{8} ) respectively, what is the probability that Xavier and Yvonne, but not Zelda,
will solve the problem?
A ( cdot frac{11}{8} )
в. ( frac{7}{8} )
c. ( frac{9}{64} )
D. ( frac{5}{64} )
E ( cdot frac{3}{64} )
12
1357Bag I contains 3 red and 4 black balls
and Bag II contains 4 red and 5 black
balls. Two balls are transferred at
random from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find
the probability that the transferred balls were both black
12
1358The probability distribution function of a random variable ( boldsymbol{X} ) is given by
: 0 1.2
( boldsymbol{x}_{i} )
[
10 c quad 5 c-1
]
( 3 c )
where ( c>0 . ) Find ( c )
12
1359If ( A ) and ( B ) are two Mutually Exclusive events in a sample space S such that
( boldsymbol{P}(boldsymbol{B})=2 boldsymbol{P}(boldsymbol{A}) ) and ( boldsymbol{A} cup boldsymbol{B}=boldsymbol{S} ) then
( boldsymbol{P}(boldsymbol{A})= )
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{4} )
D. 5
12
1360What is the probability that a leap year selected at random
will contain 53 sundays?
(6) 2
11
13619.
A bag has 4 red balls and 2 yellow balls. (The balls are
identical in all respects other than colour). A ball is drawn
from the bag without looking into the bag.
What is probability of getting a red ball? Is it more or less
than getting a yellow ball?
11
1362A four-digit number is formed by using the digits 1,2,4,8 and 9 without repitition. If one number is selected from those numbers, then what is the
probability that it will be an odd number
?
A ( frac{1}{5} )
B. ( frac{2}{5} )
( c cdot frac{3}{5} )
D. ( overline{5} )
12
1363The probability of an event that is certain to happen is ( _{–}-_{-} ? )
A . 1
B. 2
( c .3 )
( D )
12
1364( boldsymbol{8} boldsymbol{p}(boldsymbol{A} cap overline{boldsymbol{B}}) )12
1365Three cards are drawn from a bag
containing ( mathrm{m} ) cards marked ( 1,2,3 ldots . . n ) The probability that they form a
sequence is
A ( cdot frac{6}{n(n-1)} )
B. ( frac{3}{n(n-3)} )
c. ( frac{12}{n(n-2)} )
D. ( frac{3}{n(n-1)} )
12
1366UUес.
1.
If M and N are any two events, the probability that exactly
one of them occurs is
(1984 – 3 Marks)
(a) P(M)+ P(N) – 2P(M ON)
(b) P(M) + P(N)-P(MON)
(C) P(Mº)+ P(NC) -2P(
M NC)
(d) P(MONO)+P(M°ON)
11
1367Three numbers are chosen at random
withoutreplacement from the set of integers ( 1,2,3, ldots .10 . ) The probability that the minimum of thechosen
numbers is 3 or the maximum of
thechosen numbers is ( 7, ) is equal to
A . ( 23 / 120 )
B. ( 13 / 120 )
c. ( 13 / 60 )
D. ( 11 / 40 )
12
1368Evaluate ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B}), ) if ( boldsymbol{2} boldsymbol{P}(boldsymbol{A})= )
( boldsymbol{P}(B)=frac{boldsymbol{5}}{13} ) and ( boldsymbol{P}(boldsymbol{A} / B)=frac{2}{5} )
12
1369The probability that a person will get an electric contract is ( frac{2}{5} ) and the
probability that he will not get plumbing contract is ( frac{4}{7} . ) If the probability of getting at least one contract is ( frac{2}{3}, ) then the probability that he will get both is ( frac{17}{105} )
A. True
B. False
12
1370The blood groups of 30 students of Class VIII are recorded as follows:
( boldsymbol{A}, boldsymbol{B}, boldsymbol{O}, boldsymbol{O}, boldsymbol{A} boldsymbol{B}, boldsymbol{O}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O} )
( boldsymbol{A}, boldsymbol{A B}, boldsymbol{O}, boldsymbol{A}, boldsymbol{A}, boldsymbol{O}, boldsymbol{O}, boldsymbol{A B}, boldsymbol{B}, boldsymbol{A}, boldsymbol{O}, boldsymbol{B}, boldsymbol{A} )
Use this table to determine the
probability that a student of this class, selected at random, has blood group
( A B )
12
1371Three six-faced dice are thrown
together. The probability that the sum of the numbers appearing on the dice is
( k(9 leq k leq 14) ) is
( ^{text {A } cdot} frac{21 k-k^{2}-83}{216} )
B. ( frac{k^{2}-3 k+2}{432} )
c. ( frac{21 k-k^{2}-83}{432} )
D. None of these
12
1372appeared in a test of 100 marks in the subject of social
studies and the data about the marks
secured is as below:
begin{tabular}{cc}
Marks secured & Number of Students \
hline ( 0-25 ) & 50 \
( 26-50 ) & 220 \
hline ( 51-75 ) & 100 \
Above 75 & 30 \
Total number of students & 400 \
hline
end{tabular} If the result card of a student he picked
up at random, what is the probability
that the student has secured more than
50 marks.
A. 0.586
B. 0.75
c. 0.325
D. 0.1
12
1373The experiment is to randomly select a human and measure his or her length.
Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these
12
1374An examination consists of 8 questions in each of which the candidate must
say which one of the 5 alternatives is
correct one. Assuming that the student has not prepared earlier choose for each
of the question any one of 5 answer with equal probability.
(i) Prove that the probability that he gets more than one correct answer is
( left(5^{8}-3 times 4^{8}right) / 5^{8} )
(ii) Find the probability that he gets
correct answer to ( x ) or more questions.
(iii) Find the standard deviation of this
distribution.
12
1375NOVI CSC.
Two events A and B have probabilities 0.25 and 0.50
respectively. The probability that both A and B occur
simultaneously is 0.14. Then the probability that neither A
nor B occurs is
(1980)
(a) 0.39 (b) 0.25 (c) 0.11 (d) none of these
11
1376An urn contains 5 red marbles, 4 black
marbles and 3 white marbles. Then the number of ways in which 4 marbles can
be drawn so that the most three of them
are red is
12
1377Three numbers are chosen at random
withput replacement from ( {1,2, ldots, 15} )
Let ( E_{1} ) be the event that minimum of
the chosen numbers is 5 and ( E_{2} ) their
maximum is 10 then
This question has multiple correct options
( ^{mathbf{A}} cdot Pleft(E_{1}right)=frac{9}{91} )
( ^{mathrm{B}} cdot Pleft(E_{2}right)=frac{36}{455} )
( ^{mathbf{C}} cdot Pleft(E_{1} cap E_{2}right)=frac{4}{455} )
( Pleft(E_{1} mid E_{2}right)=frac{1}{9} )
12
1378If ( P(A cup B)=frac{3}{4} ) and ( P(bar{A})=frac{2}{3}, ) then
find the value of ( boldsymbol{P}(overline{boldsymbol{A}} cap boldsymbol{B}) )
A ( cdot frac{3}{2} )
B. ( frac{1}{2} )
c. ( frac{5}{12} )
D. None of these
12
1379In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear.
A ( cdot frac{11}{36} )
в. ( frac{5}{18} )
c. ( frac{13}{18} )
D. ( frac{3}{16} )
12
1380A has 3 shares in a lottery in which
there are 3 prizes and 6 blanks; ( B ) has 1 share in a lottery in which there is 1
prize and 2 blanks: show that ( A^{prime} s )
chance of success is to B’s as 16 to 7
12
1381For the three events ( A, B ) and ( C, P )
(exactly one of the events ( boldsymbol{A} ) or ( boldsymbol{B} ) occurs ( )=P(text { exactly one of the events } B ) or ( C text { occurs })=P( ) exactly one of the events ( C text { or } A text { occurs })=p ) and ( P( ) all the
three events occur simultaneously) ( = )
( p^{2}, ) where ( 0<p<1 / 2 . ) Then the
probability of at least one of the three events ( A, B ) and ( C ) occurring is
( ^{mathrm{A}} cdot frac{3 p+2 p^{2}}{2} )
( ^{text {В } cdot frac{p+3 p^{2}}{4}} )
c. ( frac{p+3 p^{2}}{2} )
( frac{3 p+2 p^{2}}{4} )
12
1382From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
A ( cdot frac{2}{52} )
в. ( frac{1}{52} )
c. ( frac{2}{13} )
D. ( frac{1}{26} )
12
1383If ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5 5}, boldsymbol{P}(boldsymbol{C})= )
( mathbf{0 . 5}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=boldsymbol{x}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{C})= )
( mathbf{0 . 4 5}, boldsymbol{P}(boldsymbol{B} cap boldsymbol{C})=mathbf{0 . 3} ) and ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B} cap )
( C)=0.2, ) then
A. ( 0.2 leq x leq 0.45 )
в. ( 0.2 leq x leq 0.5 )
c. ( 0.2 leq x leq 0.65 )
D. ( 0.2 leq x leq 1 )
12
1384A biased coin is tossed twice.The
probability of head is twice the tail.The PDF of number of heads is
( begin{array}{llll}mathbf{x} & mathbf{0} & mathbf{2} & mathbf{2}end{array} )
( p(x) quad frac{a}{d} quad frac{b}{d} quad frac{c}{d} )
then values of ( a, b, c, d ) are
A. ( a=1, b=2, c=3, d=4 )
В. ( a=1, b=4, c=4, d=9 )
c. ( a=1, b=4, c=4, d=10 )
D. ( a=1, b=2, c=1, d=4 )
12
1385Roll a fair die twice. Let ( A ) be the even
that the sum of the two rolls equals six,
and let ( B ) be the even that the same
number comes up twice. What is ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) ? )
A ( cdot frac{1}{6} )
в. ( frac{5}{6} )
( c cdot frac{1}{5} )
D. none of these
12
1386Which of the following is NOT a random experiment?
A. Rolling an unbiased dice
B. Tossing a fair coin
c. Drawing a card from a well shuffled pack of 52 card
D. None of these
12
1387Opinion No. of students
135
dislike
To know the opinion of the students about the subject statistics, a survey of
200 students was conducted. The data
is recorded in the following table.
Find the probability that a student
chosen at random
(i) likes statistics
(ii) does not like it.
12
1388Which of the following is a correct statement about probability?
A. It must have a value between -1 and 1
B. It is the collection of multiple experiments
c. Result can be in the form of decimal or negative
D. The probability of an event will not be less than 0
12
1389India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points
1,2,3 are 0.45,0.05 and 0.50
respectively. Assuming that outcomes are independent, the probability of India getting at least 7 points is
A .0 .0624
B. 0.0875
c. 0.8750
D. 0.0250
12
1390If the probability of defective bolts is
( 0.1, ) find the mean and standard
deviation for the distribution of
defective bolts in a total of 500 bolts.
12
1391fin a binomial distribution the mean is
20, standard deviation is ( sqrt{15}, ) then ( p= )
A ( cdot frac{3}{4} )
B. ( frac{1}{4} )
( c cdot frac{1}{2} )
D.
12
1392If ( A ) and ( B ) are two mutually exclusive
events then ( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})= )
A. ( P(A) . P(B) )
в. ( P(A) )
c. 0
D.
12
1393Consider the word ( W= )
MISSISSIPPI Number of ways in
which the letters of the word ( W ) can be
arranged if at least one vowel is separated from rest of the vowels
A ( frac{8 ! .16 !}{4 ! 4 ! ! 2 !} )
в. ( frac{8 ! .16 !}{4.4 ! .2 !} )
c. ( frac{8 ! .16 !}{4 ! .2 !} )
D. ( frac{8 !}{4 ! .2 !} cdot frac{165}{4 !} )
12
1394Two events ( A ) and ( B ) are such that
( P(A)=frac{1}{4}, P(A mid B)=frac{1}{4} ) and ( P(B mid A)= )
( mathbf{1} )
( overline{2} )
Consider the following statements:
(I) ( P(bar{A} mid bar{B})=frac{3}{4} )
(II) ( A ) and ( B ) are mutually exclusive
( (| I) P(A mid B)+P(A mid bar{B})=1 )
Then
A. Only (I) is correct
B. Only (I) and (II) are correct
C. Only (I) and (III) are correct
D. Only (II) and (III) are correct
12
1395If ( A, B ) and ( C ) are mutually exclusive and exhaustive events, then ( boldsymbol{P}(boldsymbol{A})+ )
( P(B)+P(C) ) equals to
A ( cdot frac{1}{3} )
B. 1
( c .0 )
D. Any value between 0 and 1
12
1396Sita and Geta are friends, what is the
probability that both will have different birthdays (ignoring a leap year)
A ( cdot frac{1}{365} )
в. ( frac{1}{364} )
c. ( frac{364}{365} )
D. None of these
12
1397A fair die is thrown two times. Find the
chance that
Product of the numbers on the
uppermost face is 12.
12
1398Find the probability of successes in
toss of a die, where a success is defined
as
(i) Number greater than 4
(ii) Six appears on die
12
1399Box I contains two white and three black
balls. Box II contains four white and one
black balls and box III contains three
white and four black balls. A dice having
three red, two yellow and one green face,
is thrown to select the box. If red face
turns up, we pick up box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the
ball drawn is white, what is the
probability that the dice had turned up with a red face?
12
1400A radar unit is used to measure speeds
of cars on a motorway. The speeds are normally distributed with a mean of 9
( mathrm{km} / mathrm{hr} ) and a standard deviation of 10
km/hr. What is the probability that a car picked at random is travelling at
more than ( 100 mathrm{km} / mathrm{hr} ? )
A .0 .1698
B. 0.1548
c. 0.1587
D. 0.1236
12
1401There are 4 white and 3 black balls in a
box. In another box there are 3 white and
4 black balls. An unbiased dice is rolled.
If it shows a number less than or equal
to
( 3, ) then a ball is drawn from the first
box, but if it shows a number more than
3 , then a ball is drawn from the second
box. If the ball drawn is black, then the
probability that the ball was drawn from the first box is
A ( cdot frac{1}{2} )
B. ( frac{6}{7} )
( c cdot frac{4}{7} )
D. 3 7
12
1402If ( mathrm{M} ) and ( mathrm{N} ) are any two events, the
probability that atleast one of them
occurs is
A ( cdot P(M)+P(N)-2 P(M cap N) )
B . ( P(M)+P(N)-P(M cap N) )
c. ( Pleft(M^{c}right)+Pleft(N^{c}right)-2 Pleft(M^{c} cap N^{c}right) )
D – ( Pleft(M cap N^{c}right)-Pleft(M^{c} cap Nright) )
12
1403Four cards are drawn at a time from a
pack of 52 playing cards. Find the probability of getting all the 4 cards of the same suit.
A ( cdot frac{44}{4165} )
В. ( frac{11}{4165} )
c. ( frac{22}{4165} )
D. none of these
12
1404Choosing a queen from a deck of cards
is an example of
A. compound event
B. complementary event
c. simple event
D. impossible event
12
1405Two coins are tossed simultabeously.
Find the probability of getting:
(i) at least one Tail
(ii) atmost two Head
(iii) one Head
12
1406If the integers ( m ) and ( n ) are chosen at
random from 1 to 100 then the
probability that ( 7^{m}+7^{n} ) is divisible by
5 is ( ? )
A. ( 1 / 5 )
B. 1/7
c. ( 1 / 4 )
D. 1/49
12
1407Suppose there are three urns
containing 2 white and 3 black balls: 3 white and 2 black balls, and 4 white and
one black ball respectively. There is equal probability of each urn being chosen. One ball is drawn from an urn
chosen at random. The probability that a white ball is drawn is ( frac{k}{15} . ) Find the
value of ( k )
12
1408A coin is tossed three times, where
(i) ( E: ) head on third toss, ( F: ) heads on
first two tosses
(ii) ( E: ) at least tow heads, ( F: ) at most
two heads
(iii) ( E: ) at most two tails, ( F: ) at least
one tail
Determine ( boldsymbol{P}(boldsymbol{E} mid boldsymbol{F}) )
A. 0.42,0.50,0.85
В. 0.50,0.42,0.85
c. 0.85,0.42,0.30
D . .0.42, 0.46, 0.47
12
1409( X ) has three children in his family. What is the probability that all the three children are boys?
A ( cdot frac{1}{8} )
B. ( frac{1}{2} )
( c cdot frac{1}{3} )
D. ( frac{3}{8} )
12
1410If ( A ) and ( B ) are two events such that
( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then
( ^{mathrm{A}} cdot P(A cup B) geq frac{3}{4} )
в. ( Pleft(A^{prime} cap Bright) leq frac{1}{4} )
c. ( frac{3}{8} leq P(A cap B) leq frac{5}{8} )
D. All of the above
12
1411When two dice are rolled, find the
probability of getting a greater number on the first die than the one on the
second, given that the sum should equal 8
A ( cdot frac{1}{5} )
B. ( frac{2}{5} )
( c cdot frac{3}{5} )
D. None of these
12
1412A biased coin (with probability of
obtaining a Head equal to ( p>0 ) ) is tossed repeatedly and independently until the first head is observed.

Compute the probability that the first head appears at an even numbered
toss.
A ( cdot frac{2-p}{3-p} )
в. ( frac{1-p}{3-p} )
c. ( frac{1-p}{2-p} )
D. none of these

12
1413“The occurrence of one event excludes
the occurrence of another event”. In a
random experiment of probability theory, it is called
A. Complementray event
B. Impossible event
c. Mutually exclusive event
D. certain event
12
1414Let ( boldsymbol{E}, boldsymbol{F}, boldsymbol{G} ) be pairwise independent events with ( P(G)>0 ) and ( P(E cap F cap )
( G)=0 . ) Then ( Pleft(E^{prime} cap F^{prime} mid Gright) ) equals
( mathbf{A} cdot Pleft(E^{prime}right)+Pleft(F^{prime}right) )
B . ( Pleft(E^{prime}right)-Pleft(F^{prime}right) )
c. ( Pleft(E^{prime}right)-P(F) )
D. ( P(E)-Pleft(F^{prime}right) )
12
1415Given that ( boldsymbol{X} sim boldsymbol{B}(boldsymbol{n}=mathbf{1 0}, boldsymbol{p}) . ) If
( boldsymbol{E}(boldsymbol{X})=mathbf{8}, ) then the value of ( boldsymbol{p} ) is
A . 0.6
в. 0.7
c. 0.8
D. 0.4
12
1416A man is know to speak the truth 3 out
of 4 times. He throws a die and reports
that it is a six. the probability that it is actually a six is
A ( cdot frac{3}{8} )
B. ( frac{1}{5} )
( c cdot frac{3}{4} )
D. None of these
12
1417Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.12
1418A coin is tossed three times. Find
( P(A / B) ) in given cases:
( A= ) Heads on third tossed, ( B= ) Heads
on first two tosses
12
1419From 3 boys ( & 2 ) girls,commit a of 2 people is to be made. Then probability of minimum 1 boy in the committee is?12
1420( X ) is a Normally distributed variable
with mean ( =30 ) and standard deviation
( =4 . ) Find ( P(x>21) )
A . 0.9878
B. 0.9383
c. 0.9975
D. 0.9126
12
1421A box contains 32 coloured marbles. 8 of
them are red marbles and the rest are
either blue or green marbles. A marble is drawn at random. Calculate the
probability of drawing a marble which is not red in colour.
( A cdot frac{2}{3} )
в. ( frac{5}{8} )
( c cdot frac{3}{4} )
D. ( frac{7}{16} )
12
1422In a series of 3 one-day cricket matches between teams ( A ) and ( B ) of a college, the probability of team A winning or drawing are ( 1 / 3 ) and ( 1 / 6 ) respectively. If a
win, loss or draw gives 2,0 and 1 point
respectively, then what is the
probability that team A will score 5
points in the series?
A ( cdot frac{17}{18} )
B. ( frac{11}{12} )
( c cdot frac{1}{12} )
D. ( frac{1}{18} )
12
1423If it rains a dealer in rain coats can earn
Rs.500/- a day. If it is fair he will lose Rs. ( 40 /- ) a day. His mean profit if the probability of a fair day is 0.6 is:
A. Rs. ( 230 /- )
B. Rs. ( 460 /- )
c. Rs. ( 176 /- )
D. Rs. 88/-
12
1424A man takes a step forward with
probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step
away from the starting point.
A .0 .368
B. 0.147
c. 0.22
D. 0.073
12
1425Q Type your question
Leagur Iuuchan a vaic, yuu unotive someone who is clearly supporting
Manchester United in the game. What is the probability that they were actually born within 25 miles of Manchester?
Assume that:
( Longrightarrow ) the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is ( frac{1}{20}, ) and
( Longrightarrow ) the chance that a person born within 25 miles of Manchester
actually supports United is ( frac{7}{10} )
( Longrightarrow ) the probability that a person not born within 25 miles of
Manchester supports United with probability ( frac{1}{10} )
A ( cdot frac{7}{26} )
в. ( frac{8}{26} )
c. ( frac{9}{26} )
D. ( frac{10}{26} )
12
1426The probability for a randomly chosen month to have its ( 10^{t h} ) day as Sunday,
is.
A ( cdot frac{1}{84} )
в. ( frac{10}{12} )
c. ( frac{10}{84} )
D.
12
1427The probability that a man hits a target is ( frac{3}{4} . ) If tried 5 time, the probability that he will hit the target at least three
times,is
A ( cdot frac{918}{10184} )
B. ( frac{884}{10244} )
c. ( frac{924}{1024} )
( D cdot frac{848}{1024} )
12
1428A pair of dice is thrown 5 times. If getting a doublet is considered as a success, then find the mean and
variance of successes.
12
1429A policeman fires four bullets at a dacoit. The probability that the dacoit will be killed by one bullet is ( 0.6 . ) What is the probability that the dacoit is still alive?
A .0 .064
B. 0.0256
c. 0.32
D. 0.16
12
1430Suppose that ( 5 % ) of men and ( 0.25 % ) of women have grey hair. A grey haired person is selected at random. What is
the probability of this person being male ? Assume that there are equal number of males and females.
12
1431Suppose we throw a dice once?
(i)What is the probability of getting a
number greater than ( 4 ? )
12
1432LUDO
In a test, the marks obtained by 15 students are 43, 73, 44,
93, 54, 64, 53, 24, 84, 40, 93, 33, 34, 74, 44. The probability
that a pupil chosen at random passed the test, if the passing
marks are 40 is
(a) 8/15
(b) 4/5
(c) 7/15
(d) 48/60
d umhare from 1 to
1
11
1433An integer is chosen at random from the
first 200 numbers.What is the
probability that the integer chosen is divisible by 6 or 8.
12
1434In a class of 100 students, 60 students
drink tea, 50 students drink coffee and
30 students drink both. A student from
class is selected at random, find the
probability that student takes at least one of the two drinks (i.e. tea or coffee or both)
( A cdot 1 )
5
B. ( frac{2}{5} )
( c cdot frac{3}{5} )
D. ( frac{4}{5} )
12
1435A random variable ( X ) has its range ( X= )
{3,2,1} with the probabilities, ( frac{1}{2}, frac{1}{3} ) and ( frac{1}{6} ) respectively. The mean
value of ( X ) is
A ( cdot frac{5}{3} )
B. ( frac{7}{3} )
( c .3 )
( D )
12
1436If ( A ) and ( B ) are events such that ( P(A)= ) ( frac{1}{2}, P(B)=frac{1}{3} ) and ( P(A cap B)=frac{1}{4}, ) then
find ( boldsymbol{P}(boldsymbol{A} / boldsymbol{B}) )
12
1437In a bolt factory, machines ( A, B ) and ( C )
manufacture ( 25 %, 35 %, 40 % )
respectively. Of the total of their output ( 5 %, 4 % ) and ( 2 % ) are defective. A bolt is
drawn and is found to be defective.
What are the probabilities that it was
manufactured by the machines ( A, B, C )
( mathbf{A} cdot frac{25}{69}, frac{28}{69}, frac{16}{69} )
B. ( frac{28}{69}, frac{25}{69}, frac{16}{69} )
C ( cdot frac{25}{69}, frac{16}{69}, frac{28}{69} )
D. ( frac{16}{69}, frac{28}{69}, frac{25}{69} )
12
1438If two dice are rolled 12 times, obtain the mean and the variance of the
distribution of successes, if getting a total greater than 4 is considered a
success.
12
1439An urn contains 25 balls of which 10
bear a mark ‘ ( X ) ‘ and the remaining 15
bear a mark ‘Y’. A ball is drawn at
random from the urn, its mark noted
down and it is replaced. If 6 balls are drawn in this way, find the probability that
(i) All will bear mark ‘ ( boldsymbol{X} )
(ii) Not more than two will bear ‘ ( Y ) ‘ mark
12
1440Let ( S={1,2, ldots ., 20} . ) A subset ( B ) of ( S ) is said to be “nice”, if the sum of the elements of ( B ) is ( 203 . ) Then the
probability that a randomly chosen subset of ( S ) is “nice” is:
A ( cdot frac{6}{2^{20}} )
в. ( frac{5}{2^{20}} )
c. ( frac{4}{2^{20}} )
D. ( frac{7}{2^{20}} )
12
1441There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three
questions have 4 choices each and the
next three have 2 each?
12
1442Two persons ( A ) and ( B ) are throwing an
unbiased six faced die alternatively, with the condition that the person who
throws 3 first wins the game. If ( A ) starts the game, the probabilities of ( A ) and ( B ) to win the same are respectively
A ( cdot frac{6}{11}, frac{5}{11} )
в. ( frac{5}{11}, frac{6}{11} )
c. ( frac{8}{11}, frac{3}{11} )
D. ( frac{3}{11}, frac{8}{11} )
12
1443Given two mutually exclusive events ( boldsymbol{A} ) and ( B ) such that ( P(A)=frac{1}{2} ) and ( P(B)=frac{1}{3}, ) find ( P(A text { or } B) )
A ( cdot frac{3}{5} )
в. ( frac{5}{6} )
( c cdot frac{4}{5} )
D. None of these
12
1444Of the students in a college, it is known
that ( 60 % ) reside in hostel and ( 40 % ) are
day scholars.Previous year results report that ( 30 % ) of all students who
reside in hostel attain ‘A’ grade and ( 20 % ) of day scholars attain ‘A’ grade in their
annual examination. At the end of the
year, one student is chose at random
from the college and he has an ‘A’ grade, what is the probability that the student is a hostlier?
12
1445For ( i=1,2,3,4 ) let ( T_{i} ) denote the event
that the students ( S_{i} ) and ( S_{i+1} ) do NOT sit adjacent to each other on the day of the examination. Then the probability of the
event ( boldsymbol{T}_{mathbf{1}} cap boldsymbol{T}_{mathbf{2}} cap boldsymbol{T}_{mathbf{3}} cap boldsymbol{T}_{mathbf{4}} ) is?
A ( cdot frac{1}{15} )
в. ( frac{1}{10} )
c. ( frac{7}{60} )
D.
12
1446A die is thrown. Write the sample space.
If ( A ) is the event that the number is less
than four, write the event ( boldsymbol{A} ) using set
notation.
12
1447f ( mathrm{E} ) and ( mathrm{F} ) are independent events then:
This question has multiple correct options
A. E & F mutually exclusive
B. E & ( bar{F} ) (complement of the event ( F ) ) are independent
C ( . bar{E} & bar{F} ) are independent
D ( . P(E / F)+P(bar{E} / F)=1 )
12
1448Four letters mailed today each have a
probability of arriving in two days or sooner equal to ( frac{2}{3} . ) Calculate the probability that exactly two of the four letters will arrive in two days or sooner.
( mathbf{A} cdot frac{4}{81} )
B. ( frac{16}{81} )
c. ( frac{6}{27} )
D. ( frac{8}{27} )
E ( cdot frac{4}{9} )
12
1449There are two balls in an urn whose
colors are not known ( ball can be either
white or black). A white ball is put into
the urn. A ball is then drawn from the
urn. The probability that it is white is
A ( cdot frac{1}{4} )
B. ( frac{1}{3} )
( c cdot frac{2}{3} )
D.
12
1450What is called one or more outcomes of
an experiment?
A. Space
B. Experiment
c. sample
D. Event
12
1451Bag ( I ) contains 3 red and 4 black balls
and Bag ( I I ) contains 4 red and 5 black
balls. One ball is transferred from Bag ( boldsymbol{I} ) and Bag ( I I ) and then a ball is drawn
from Bag ( I I . ) The ball so drawn is found
to be red in colour. Find 310 times the
probability that the transferred ball is
black.
12
1452An unbiassed die is toossed. Find the
probability that it is a multiple of 3
12
1453( A ) is known to speak truth 3 times out of
5 times. He throws a dice and reports
that it is a one. Find the probability that it is actually one.
12
1454A bag contains n white and n red balls.
Pairs of balls are drawn without
replacement until the bag is empty. Show that the probability that each pair consists of one white and one red ball is
( frac{mathbf{2}^{n}}{2 n} mathbf{C}_{n} )
12
1455If ( A ) and ( B ) are two mutually exclusive
events, then This question has multiple correct options
A ( . P(A) leq P(bar{B}) )
в. ( P(A)>P(B) )
c. ( P(B) leq P(bar{A}) )
( D(A)<P(B) )
12
1456A bag contains 9 marbles, 3 of which
are red, 3 of which are blue, and 3 of
which are yellow. If three marbles are
selected from the bag at random, what is probability that they are all of different colors?
A ( cdot frac{1}{15} )
в. ( frac{9}{28} )
c. ( frac{1}{19} )
D. ( frac{1}{20} )
12
1457Two fair die are thrown. The probability the sum of the numbers appearing is 6
is
A ( cdot frac{1}{6} )
в. ( frac{5}{6} )
c. ( frac{1}{36} )
D. ( frac{5}{36} )
12
1458The probability that a leap year not to contain 53 Sundays is.12
1459How many 4 -digit numbers can be
formed from digit 1,1,2,2,3,3,4,4,5,5
( ? )
12
1460Expected number of heads when we toss ( n ) unbiased coins is
( mathbf{A} cdot 2 n )
в. ( n )
( c cdot frac{n}{2} )
D. ( frac{n}{4} )
12
1461A card from a pack of 52 cards is lost.
From the remaining cards of the pack,
two cards are drawn and are found to be
both diamonds. If the probability of the lost card is a diamond is ( boldsymbol{p} ) enter ( mathbf{1 0 0} boldsymbol{p} )
12
1462Given that ( A subset B, ) then identify the
correct statement
( mathbf{A} cdot P(A / B)=P(A) )
B ( . P(A / B) leq P(A) )
( mathbf{c} cdot P(A / B) geq P(A) )
D ( cdot P(A / B)=P(A)-P(B) )
12
1463The probability that at least one of the events A and B occurs
is 0.6. If A and B occur simultaneously with probability 0.2,
then P(A) +P(B) is
(1987-2 Marks)
(a) 0.4 (6) 0.8 (c) 1. (d) 1.4
(e) none
(Here A and B are complements of A and B, respectively).
11
1464Four persons can hit a target correctly with probabilities ( frac{1}{2}, frac{1}{3}, frac{1}{4} ) and ( frac{1}{8} ) respectively. If all hit at the target independently, then the probability that the target would be hit, is?
A ( cdot frac{25}{192} )
в. ( frac{1}{192} )
c. ( frac{25}{32} )
D. ( frac{7}{32} )
12
1465Probability of hitting a target independently of 4 persons are ( frac{1}{2}, frac{1}{3}, frac{1}{4}, frac{1}{8} . ) Then the probability that
target is hit, is?
A ( cdot frac{1}{192} )
в. ( frac{5}{192} )
c. ( frac{25}{32} )
D. ( frac{7}{32} )
12
1466For any two events ( A ) and ( B ), the
conditional probability ( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})= )
( frac{P(B cap A)}{P(A)} ) and ifAand ( B ) are independent
( boldsymbol{P}(boldsymbol{B} cap boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) cdot boldsymbol{P}(boldsymbol{A}) ) So,
( boldsymbol{P}(boldsymbol{B} / boldsymbol{A})=boldsymbol{P}(boldsymbol{B}) )
A lot contains 50 defective and 50 non-
defective bulbs. Two bulbs are drawn at
random one at a time with replacement. The events ( A, B, C ) are defined as:
( mathbf{A}: ) 1st bulb is defective
( mathrm{B}: ) 2nd bulb is non-defective
( mathrm{C}: ) both are defective or both are non-
defective
then,
A. A, B, C are pair-wise independent as well as mutually independent
B. A, B, C are pair-wise independent but mutually not
c. ( A, B, C ) are mutually independent but pair-wise not
D – of these
12
1467Three coins are tossed describe
(i) Two events which are mutually exclusive
(ii) Three events which are mutually exclusive and exhaustive
(iii) Two events which are not mutually
exclusive
(iv) Two events which are mutually exclusive but not exhaustive
(v) Three events which are mutually exclusive but not exhaustive
12
1468A fair coin is tossed at a fixed number
of times. If the probability of getting exactly 3 heads equals the probability
of getting exactly 5 heads, then the probability of getting exactly one head
is
A ( cdot frac{1}{64} )
в. ( frac{1}{32} )
c. ( frac{1}{16} )
D.
12
1469If ( A ) and ( B ) are independent events such that ( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 6}, boldsymbol{P}(boldsymbol{A})=mathbf{0 . 2}, ) find
( P(B) )
12
1470Suppose that of all used cars of a particular year ( 30 % ) have bad brakes.
You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked.
The chance that the mechanic will give you the wrong report is ( 20 % ). Assuming that the car you take to the mechanic is selected at random from the population
of cars of that year. The chance that the
car’s brakes are good, given that the mechanic says its brakes are good, is
A ( frac{28}{130} )
в. ( frac{29}{31} )
c. ( frac{37}{62} )
D. ( frac{29}{62} )
12
1471What is the probability of getting a king if a card is drawn from a pack of 52
cards?
A ( cdot frac{1}{52} )
в. ( frac{2}{52} )
c. ( frac{3}{52} )
D. ( frac{4}{52} )
12
1472Rahim takes out all the hearts from the
cards. What is the probability of Picking out an ace from the remaining
pack.
12
1473he horses a
Kr. A seleder
Five horses are in a race. Mr. A selects two of the home
random and bets on them. The probability that Mr. A sel
the winning horse is
12003
11
1474P
11.
Sol.
Total number of outcomes 25
Find the probability of getting a number less than 5 in a single throw of an
Total number of outcomes = 6
11
1475A bag contains 4 balls.Two balls drawn at random without replacement and are
found to be white. What is the
probability that all balls are white?
12
1476A sum of money is rounded off to the nearest rupee. The probability that the round off error is at least ten paisa is ( frac{9 k}{100} . ) The value of ( k ) is12
1477A box contain ( N ) coins, ( m ) of which are
fair and rest are biased. The probability of getting a head when a fair coin is tossed is ( frac{1}{2}, ) while it is ( frac{2}{3} . ) when a biased coin is tossed. A coin is drawn from the
box at random and is tossed twice. The
first time it shows head and the second
time it shows tail. The probability that the coin drawn is fair is
A ( cdot frac{8 mathrm{m}}{8 mathrm{N}+mathrm{m}} )
B. ( frac{mathrm{m}}{8 mathrm{N}+mathrm{m}} )
c. ( frac{9 mathrm{m}}{8 mathrm{N}+mathrm{m}} )
D. ( frac{9 mathrm{N}}{8 mathrm{N}+mathrm{m}} )
12
1478A coin is tossed 3 times, the total number of possible outcomes is:
A . 3
B. 4
( c .6 )
( D )
12
1479To define probability disribution function we assign to each variable
A. the respective probabilities
B. the specific random values
c. some integers
D. none
12
1480Suppose that the letter cards for the word ( M ) ATHEMATICS were putt
face down and mixed up and a card is
picked up at random. What is the probability of picking up a vowel?
12
1481A biased coin with probability ( P,(0<p< )
1) of heads is tossed until a head
appear for the first time. If the
probability that the number of tosses
required is even is ( frac{2}{5} ) then ( P= )
( A cdot frac{2}{5} )
B.
( c cdot frac{1}{3} )
( D cdot frac{3}{5} )
12
1482A card is drawn from the pack of 25
cards labelled with numbers 1 to 25
Write the sample space for this random experiment.
12
1483The probability of an ordinary year
having 53 Tuesdays is:
A ( cdot frac{2}{7} )
B. ( frac{1}{7} )
( c cdot frac{3}{7} )
D.
12
1484A die is thrown once. What is the
probability of getting a number less
than ( 3 ? )
12
1485At random all the letters of the word
“ARTICLE” are arranged in all possible ways. The probability that the arrangement begins with vowel and ends with a consonant is
A . ( 1 / 7 )
в. ( 2 / 7 )
c. ( 3 / 7 )
D. ( 4 / 7 )
12
1486A company has two plants to manufacture televisions. The plant
manufacture ( 70 % ) of televisions and
plant II manufacture ( 30 % . ) At plant 1,80 ( % ) of the televisions are rated as of
standard quality and at plant II, ( 90 % ) of
the televisions are rated as of standard
quality. A television is chosen at random and is found to be of standard
quality. The probability that it has come from plant II is
12
1487An experiment consists of tossing a coin and then throwing it second time if
a head occurs. If a tail occurs on the
first toss then a die is rolled once. Find
the sample space
12
1488If ( A ) and ( B ) are mutually exclusive such
that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3 5} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4 5} )
find
( boldsymbol{P}(boldsymbol{A} cap boldsymbol{B}) )
12
1489The probability that a student selected at random from a class will pass in Mathematics is ( 4 / 5, ) and the probability that he/she passes in Mathematics and Computer Science is ( 1 / 2 . ) What is the probability that he/she will pass in Computer Science if it is known that he has passed in Mathematics?12
1490Probability ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 7}, boldsymbol{P}(boldsymbol{B})= )
( mathbf{0 . 4}, boldsymbol{P}(boldsymbol{A} cap boldsymbol{B})=mathbf{0 . 3}, ) then ( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right) ) is
equal to
A . ( 0 . )
в. 0.3
( c .0 .2 )
D. 0.4
12
1491For a certain type of computers, the length of time between charges of the
battery is normally distributed with a
mean of 50 hours and a standard
deviation of 15 hours. John owns one of
these computers and wants to know the
probability that the length of time will
be between 50 and 70 hours.
A .0 .4082
B. 0.4025
c. 0.4213
D. 0.4156
12
1492What is ( P(Z=10) ) equal to ( ? )
( mathbf{A} cdot mathbf{0} )
в. ( 1 / 2 )
c. ( 1 / 3 )
D. ( 1 / 5 )
12
14937.
E and F are two independent events. The probability that
Don E and Fhappen is 1/12 and the probability that neither
Enor F happens is 1/2. Then,
(1993 – 2 Marks)
(a) P(E)=1/3,P(F)=1/4
(b) P(E)=1/2,P(F)=1/6
(c) P(E)=1/6, P(F)= 1/2
(d) P(E)=1/4, P(F)=1/3
12
1494A bag contains 10 red balls and 8 green balls. 2 balls are drawn at random one
by one with replacement. Find the probability that both the balls are green that a second year student is chosen.
12
1495A coin is tossed until a head appears or
it has been tossed 3 times. Given that
head does not appear on the first toss, the probability that the coin is tossed 3 times is
A ( cdot frac{1}{4} )
B. ( frac{3}{8} )
( c cdot frac{1}{8} )
D.
12
1496A biased coin with probability ( boldsymbol{p}, boldsymbol{0}< ) ( p<1, ) of heads is tossed until a head
appears for the first time. If the probability that the number of tosses required is even is ( 2 / 5, ) then ( p=dots )
A. ( 2 / 5 )
B. ( 2 / 3 )
c. ( 1 / 3 )
D. ( 3 / 5 )
12
1497A tyre manufacturing company kept a record of the distance covered before a
tyre needed to be replaced. The table
show the result of 1000 cases :
Distance in ( K m quad ) Frequency
Less than 4000 20
4000 to 9000 210
9000 to 14000 325
More than 14000 445
If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between ( 4000 mathrm{km} ) and ( 14000 mathrm{km} ) ?
A . 0.65
B. 0.625
c. 0.125
D. None of these
12
1498If ( A, B ) be two events such that ( P(A cup )
( B)=frac{5}{6}, P(A cap B)=frac{1}{3} ) and ( Pleft(B^{prime}right)=frac{1}{2} )
then events ( A, B ) are
A. dependent
B. independent
c. mutually exclusive
D. none of these
12
1499If 3 coins are tossed simultaneously,
the probability of 2 heads and 1 tail is:
A ( cdot frac{5}{8} )
B. ( frac{1}{8} )
( c cdot frac{3}{8} )
D. ( frac{7}{8} )
12
1500If ( boldsymbol{P}left(boldsymbol{E}_{boldsymbol{k}}right) propto boldsymbol{k} ) for ( boldsymbol{0} leq boldsymbol{k} leq boldsymbol{n}, ) then
( lim _{n rightarrow infty} sum_{k=0}^{n} Pleft(E_{k} mid Aright) ) equals
( mathbf{A} cdot mathbf{0} )
B. ( 1 / 2 )
c. ( 1 / 6 )
( D )
12
1501Three cards are drawn at random from a
pack of 52 cards. What is the probability that all the three cards are kings?
12
1502A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor
queen?
12
1503Probability of getting 2 when we roll a
dice
12
1504One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9
black balls. One ball is taken from each
bag. What is the probability that both the balls will be of the same colour?
A ( cdot 207 / 625 )
B. ( 191 / 625 )
c. ( 23 / 625 )
D. ( 227 / 625 )
12
1505Two fair dice are tossed. Let x be the event that the first die
shows an even number and y be the event that the second
die shows an odd number. The two events x and y are:
(a) Mutually exclusive
(1979)
(6) Independent and mutually exclusive
(c) Dependent
12
1506A packet of 10 CD’s contains 4 defected. The CD’s are selected at random, one by one, examined and are not replaced. The probability that 7 th ( C D ) is the last defective is
A ( cdot frac{2}{21} )
B. ( frac{4}{9} )
c. ( frac{7}{27} )
D. None of these
12
1507( A ) and ( B ) are two independent events. The probability that both ( A ) and ( B ) occur is ( frac{1}{6} ) and the probability that neither of them occur is ( frac{1}{3} ). Then ( P(A) ) is equal to
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{5}{6} )
D. ( frac{1}{2} ) or ( frac{1}{3} )
12
1508If ( A ) and ( B ) are two events, such that ( P(A )
or ( mathrm{B} ) ) ( =mathrm{P}(mathrm{A}), ) then
A. events A and B are mutually exclusive
B. events A and B are statistically independent
c. event B is a subset of event A
D. event A is a subset of event B
12
15098.
Numbers 1 to 10 are written on ten separate slips (one
number on one slip), kept in a box and mixed well. One slip
is chosen from the box without looking into it. What is the
probability of
(1) getting a number 6?
(i) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1-digit number?
11
1510For any two events ( A ) and ( B )
This question has multiple correct options
( mathbf{A} cdot P(A cap B) geq P(A)+P(B)-1 )
B ( cdot P(A cap B) geq P(A)+P(B) )
( mathbf{c} cdot P(A cap B)=P(A)+P(B)-P(A cup B) )
D ( cdot P(A cap B)=P(A)+P(B)+P(A cup B) )
12
1511A fair die is thrown. What is the
probability that the score is not a factor
of 5?
A ( cdot frac{1}{5} )
B. ( frac{1}{3} )
( c cdot frac{5}{6} )
D. ( frac{2}{3} )
12
15124 cards are chosen from a pack of 52
playing cards? In how many of these two are red cards
and two are black cards.
12
1513A problem in mathematics is given to the
in mathematics is given to three students A, B, C
their respective probability of solving the problem
is 1.
1 1
is and Probability that the problem is solved is
[2002]
12
1514The probability of guessing the correct answer to a certain questions is ( frac{x}{2} . )
the probability of not guessing the correct answer is ( frac{3 x}{2}, ) then find the value
of ( x )
12
1515Sample space for experiment in which a
dice is rolled is
A . 4
B. 8
c. 12
D. None of these
12
1516Two probability distributions of the discrete random variable ( X ) and ( Y ) are
given below.
( boldsymbol{X} quad mathbf{0} ) 3 ( mathbf{2} )
( P(X) quad frac{1}{5} quad frac{2}{5} quad frac{1}{5} quad frac{1}{5} )
[
begin{array}{ccccc}
boldsymbol{Y} & mathbf{0} & mathbf{1} & mathbf{2} & mathbf{3} \
P(Y) & frac{1}{5} & frac{3}{10} & frac{2}{5} & frac{1}{10}
end{array}
]
Then
A.
[
Eleft(Y^{2}right)=2 E(X)
]
B.
[
Eleft(Y^{2}right)=E(X)
]
( mathbf{c} cdot E(Y)=E(X) )
( D )
[
Eleft(X^{2}right)=2 E(Y)
]
12
1517If we throw a dice, then the sample
space, ( S=1,2,3,4,5,6 . ) Now the event
of 3 appearing on the dice is simple and given by
A. ( E=2,3 )
В. ( E=1,2,3 )
c. ( E=3 )
D. ( E=1,3 )
12
1518A fair coin is tossed ( 2 n ) times. The
probability of getting as many heads in
the first ( n ) tosses as in the last ( n ) is
A ( cdot frac{2 n_{C_{n}}}{2^{2 n}} )
B. ( frac{2 n_{C_{n-1}}}{2^{n}} )
c. ( frac{n}{2^{n}} )
D. ( frac{n^{2}}{2^{n}} )
12
1519A coin is tossed 100 times and tail is
obtained 10 times. Now, if a coin is
tossed at random, what is the
probability of getting a head?
A ( cdot frac{11}{10} )
в. ( frac{9}{10} )
c. ( frac{90}{10} )
D. ( frac{100}{10} )
12
1520( A ) has 3 tickets of a lottery containing 3 prizes and 9 blanks. ( B ) has two tickets
of another lottery containing 2 prizes and 6 blanks. The ratio of their chances
of success is
A ( cdot frac{32}{55}: frac{15}{28} )
в. ( frac{32}{55}: frac{13}{28} )
c. ( frac{34}{55}: frac{13}{28} )
D. ( frac{34}{55}: frac{15}{28} )
12
1521An experiment succeeds twice as often as it fails. Find the chance that in the
next six trials, there shall be at least
four successes.
A ( cdot frac{233}{729} )
в. ( frac{64}{729} )
c. ( frac{496}{729} )
D. ( frac{432}{729} )
12
1522If
A, B are two independent events, ( P(A)=frac{3}{4} ) and ( P(B)=frac{5}{8}, ) then
( boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})= )
A ( cdot frac{3}{32} )
в. ( frac{29}{32} )
c. ( frac{15}{32} )
D. ( frac{5}{32} )
12
152319. One ticket is selected at random from 50 tickets numbered
00,01.02…., 49. Then the probability that the sum of the digits
on the selected ticket is given that the product of these
digits is zero, oquals:
(2009)
12
1524Die ( A ) has 4 red and 2 white faces
whereas die ( B ) has 2 red and 4 white
faces. A coin is flipped once. If it shows a head, the game continues by throwing die ( A, ) if it shows tail, then die ( B ) is to be
used. If the probability that die ( A ) is used is ( frac{64}{66} ) where it is given that red turns up every time in first ( n ) throws,
then ( n ) is
12
1525The contents of three bags ( I, I I ) and ( I I I )
are as follows:
Bag ( I: 1 ) white, 2 black 3 red balls
Bag ( I I: 2 ) white, 1 black 1 red balls
Bag III : 4 white, 5 black 3 red balls A bag is chosen at random and two
balls are drawn. What is the probability that the balls are white and red
12
1526A coin is tossed two times, what is the
probability of getting head at least once
12
1527Sixteen players ( boldsymbol{S}_{1}, boldsymbol{S}_{2}, ldots . boldsymbol{S}_{16} ) play in a
tournament. They are divided into eight pairs at random. From each pair a
winner is decided on the basis of a
game played between the two players of the pair. Assume that all the players are of equal strength.
The probability that the player ( S_{1} ) is among the eight winners is ( frac{1}{k} . ) Find the
value of ( boldsymbol{k} )
12
1528From a lot of 30 bulbs which include 6
defectives, a sample of 2 bulbs are drawn at random with replacement.
Find the probability distribution of the number of defective bulbs.
12
1529Out of following which are random
variables
This question has multiple correct options
A. ( x= ) “Number of heads when two coins are tossed
B. ( x= ) “Sum of digits on uppermost face of two dice
c. solution of ” ( X-4=0 ” )
D. ( x= ) “Raining
12
1530Let ( A ) and ( B ) be two events such that
( P(overline{A cup B})=frac{1}{6}, P(A cap B)=frac{1}{4} ) and
( P(bar{A})=frac{1}{4}, ) where ( bar{A} ) stands for
complement of event ( A ). Then, the
events ( A ) and ( B ) are
A. Mutually exclusive and independent
B. Independent, but not equally likely
c. Equally likely but not independent
D. Equally likely and mutually exclusive
12
1531The probability that at least one of the events ( A ) and ( B ) occur is ( 0.6 . ) If ( A ) and ( B )
occur simultaneously with probability
0.2, then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}})= )
A . 0.4
B. 0.8
c. 1.2
D. 1.
12
1532A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
12
153311.
There are four machines and it is known that exactly two 01
them are faulty. They are tested, one by one, in a random
order till both the faulty machines are identified. Then the
probability that only two tests are needed is (1998 – 2 Marks)
(a) 13 (6) 1/6 (c) 1/2 (d) 1/4
12
1534A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
12
1535A and B play a game in which ( mathbf{A}^{prime} ) s chance of winning is ( frac{1}{5} ) in a series of 6
games, the probability that A will win
all the 6 games is
( ^{mathrm{A}} cdot_{frac{6}{2} C}left(frac{1}{5}right)^{6} )
( ^{mathrm{B}} cdot_{6}^{6} Cleft(frac{1}{5}right)^{6}left(frac{4}{5}right)^{0} )
( ^{mathbf{C}} cdotleft(frac{4}{5}right)^{6} )
( ^{mathrm{D} cdot}_{^{6}} Cleft(frac{1}{5}right)^{5}left(frac{4}{5}right) )
12
1536The probability that at least one of the
events ( A ) and ( B ) occurs is ( 0.6, ) If ( A ) and ( B )
occur simultaneously with probability
0.2, then ( boldsymbol{P}(overline{boldsymbol{A}})+boldsymbol{P}(overline{boldsymbol{B}}) ) is
A. 0.4
B. 0.8
( c cdot 1.2 )
D. 1.4
12
1537There are 100 tickets in a raffle
(Lottery). There is 1 prize each of Rs. ( mathbf{1 0 0 0} /-, ) Rs. ( mathbf{5 0 0} /- ) and Rs. ( mathbf{2 0 0} /- )
Remaining tickets are blank. Find the
expected price of one such ticket.
12
1538( A ) and ( B ) alternately cut a pack of cards
which is shuffled after each cut. The
game is started by ( A ) and continuous until one of the players cuts a club. The probability that ( B ) win the game is ( k / 7 ) Find ( k )
12
1539A random variable ‘ ( X ) ‘ has the following probability distribution:
[
begin{array}{lcccc}
x=x & 0 & 1 & 2 & 3 \
P(X=x) & 0 & k & 2 k & 2 k
end{array}
]
Find:
(i) ( k )
(ii) The Mean and
(iii) ( boldsymbol{P}(boldsymbol{0}<boldsymbol{X}<mathbf{5}) )
12
1540Cards of an ordinary deck of playing cards are placed into two heaps. Heapconsists of all the red cards and heap-II
consists of all the black cards. A heap is chosen at random and a card is drawn,
find the probability that the card drawn is a king.
12
1541Identify which number cannot be a probability? This question has multiple correct options
A . ( 0 . )
B . -0.45
c. 1
D. 1.
12
1542In a building programme the event that all the materials will be delivered at the
correct time is ( M ) and the event that
the building programme will be completed on time is ( F . ) Given that ( boldsymbol{P}(M)=mathbf{0 . 8} ) and ( boldsymbol{P}(boldsymbol{M} cap boldsymbol{F})=mathbf{0 . 6 5} )
find ( boldsymbol{P}(boldsymbol{F} / boldsymbol{M}) . ) If ( boldsymbol{P}(boldsymbol{F})=mathbf{0 . 7}, ) find the
probability that the building programme will be completed on time if all the materials are not delivered at the
correct time.
( ^{mathbf{A}} cdot P(F / M)=frac{11}{16} ; P(F / bar{M})=frac{1}{6} )
B. ( P(F / M)=frac{15}{16} ; P(F / bar{M})=frac{1}{8} )
( ^{mathbf{c}} cdot P(F / M)=frac{13}{16} ; P(F / bar{M})=frac{1}{4} )
D. None of these
12
1543Let ( A ) and ( B ) be two events such that
( boldsymbol{P}left(boldsymbol{A} cap boldsymbol{B}^{prime}right)=mathbf{0 . 2 0}, boldsymbol{P}left(boldsymbol{A}^{prime} cap boldsymbol{B}right)=mathbf{0 . 1 5} )
( P(A text { and } B text { both fail })=0.10 . ) Then
This question has multiple correct options
A. ( P(A / B)=11 / 14 )
В . ( P(A)=0.7 )
c. ( P(A cup B)=0.9 )
D. ( P(A / B)=1 / 2 )
12
1544Let ( A ) and ( B ) be two finite sets having ( m )
and ( n ) elements respectively such that ( boldsymbol{m} leq boldsymbol{n} . ) A mapping is selected at random from the set of all mappings from ( A ) to ( B ). The probability that the mapping selected is an injection, is
A. ( frac{n !}{(n-m) ! m^{n}} )
в. ( frac{n !}{(n-m) ! n^{m}} )
c. ( frac{m !}{(n-m) ! n^{m}} )
D. ( frac{m !}{(n-m) ! m^{n}} )
12
1545Two balls are drawn at random with
replacement from a box containing 10 black and 8 red balls. Find the
probability that both balls are red,
12
1546An ( M B M ) applies for a job in two firms
( X ) and ( Y . ) The probability of his being selected in firm ( X ) is 0.7 and being
rejected at ( Y ) is ( 0.5 . ) The probability of at least one of his applications being
rejected is ( 0.6 . ) The probability that he will be selected in one of the firms, is
A . 0.6
B. 0.4
( c .0 .8 )
D. None of these
12
1547Suppose ( X ) has a binomial distribution ( B ) of ( 6, frac{1}{2} . ) Show that ( X=3 ) is the most likely outcome
(Hint ( : P(X=3) ) is the maximum
among all ( left.boldsymbol{P}left(boldsymbol{x}_{i}right), boldsymbol{x}_{i}=mathbf{0}, mathbf{1}, mathbf{2}, mathbf{3}, mathbf{4}, mathbf{5}, boldsymbol{6}right) )
12
1548In a construction job, following are some probabilities given:
Probability that there will be strike is ( 0.65, ) probability that the job will be completed on time if there is no strike is ( 0.80, ) probability that the job will be completed on time if there is strike is
0.32. Determine probability that the construction job will get complete on
time
A .0 .438
в. 0.538
( c cdot 0.488 )
D. None of these
12
1549In an examination hall there are four
rows of chairs. Each row has 8 chairs
one behind the other. There are two
classes sitting for the examination with
16 students in each class. It is desired
that in each row, all students belong to the same class and that no two
adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?
12
1550The below frequency distribution table
represents the blood groups of 30
students of a class. Use this table to
determine the probability that a student of this class, selected at
random, has blood group ( A B )
Blood group Number of students
( A ) 9
( B ) 6
th 3
12
Total 30
12
1551If ( A ) and ( B ) be two events associated
with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 3}, boldsymbol{P}(boldsymbol{B})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{A} )
( B)=0.6, ) then value of ( Pleft(frac{bar{A}}{B}right)+ )
( Pleft(frac{A}{bar{B}}right) ) is
( A )
в. ( frac{3}{4} )
( c cdot frac{2}{5} )
D. ( frac{13}{12} )
E. ( frac{11}{12} )
12
1552In a simultaneous throw of a pair of dice, if the probability of getting odd number on the first and 6 on the second is ( frac{1}{a} . ) Find ( a )12
1553In a village of 120 families, 93 families
use firewood for cooking, 63 families use kerosene, 45 families use cooking
gas, 45 families use firewood and kerosene, 24 families use kerosene and
cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.
A . 10
B . 15
c. 20
D. 25
12
1554( A ) and ( B ) are two independent events of
an experiment .if ( boldsymbol{P}(boldsymbol{n} boldsymbol{o} boldsymbol{t} boldsymbol{B})= )
( mathbf{0 . 6 5}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=mathbf{0 . 8 5}, ) find ( boldsymbol{P}(boldsymbol{A}) )
12
1555( A ) and ( B ) are two independent witnesses
is a case. The probability that ( A ) will speak truth is ( x ) and the probability that ( B ) will speak the truth is ( y . A ) and ( B ) agree in a certain statement. The
probability that the statement is true is
A ( cdot frac{x y}{1-x y} )
в. ( frac{x y}{1-x-y+2 x y} )
c. ( frac{2 x y}{x-y} )
D. ( frac{x y}{1-x-y} )
12
1556n an automobile factory, certain parts are to be fixed into the chassis in a
section before it moves into another
section. On a given day, one of the three persons ( A, B ) and ( C ) carries out this task. ( A ) has ( 45 % ) chance, ( B ) has ( 35 % )
chance and ( C ) has ( 20 % ) chance of doing
the task. The probability that ( A, B ) and
( C ) will take more than the allotted time is ( frac{1}{6}, frac{1}{10} ) and ( frac{1}{20} ) respectively. If it is found that the time taken is more than
the allotted time, what is the probability that ( A ) has done the task?
12
1557If ( C ) and ( D ) are two events such that
( mathbf{C} subset mathbf{D} ) and ( mathbf{P}(mathbf{D}) neq mathbf{0}, ) then the correct
statement among the following is
( ^{mathbf{A}} cdot pleft(frac{C}{D}right)=mathrm{P}(mathrm{C}) )
( ^{mathbf{B}} cdot pleft(frac{C}{D}right) geq mathrm{P}(mathrm{C}) )
( ^{c} cdot pleft(frac{C}{D}right)<mathrm{P}(mathrm{C}) )
( Pleft(frac{C}{D}right)=frac{P(D)}{P(C)} )
12
1558Given find ( boldsymbol{P}(boldsymbol{A})=frac{1}{5}, ) find ( boldsymbol{P}(boldsymbol{A} text { or } boldsymbol{B}), ) if
( A ) and ( B ) are mutually exclusive events.
12
1559On one page of a telephone directly, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example in the number 25828573
the unit place digit is 3 ) is given in table
below :
Digit
Frequency 22 26 22 22
Without looking at the page, the pencil is placed on one of these numbers, i.e., the
number is chosen at random. What is the
probability that the digit in its unit place is more than ( 7 ? )
( A )
[
0.15
]
в. 0.17
( c )
0.18
D. None of these
12
1560Three groups ( A, B, C ) are contesting for positions on the Board of Directors of a company. The probabilities of their
winning are 0.5,0.3,0.2 respectively. If
the group ( A ) wins, the probability of
introducing a new product is 0.7 and the corresponding probabilities for groups ( B ) and ( C ) are 0.6 and 0.5
respectively. The probability that the new product will be introduced is given
by
A . 0.36
в. 0.35
c. 0.63
D. 0.53
12
1561t is known that an urn containing altogether 10 balls was filled in the following manner: A coin was tossed 10 times, and according as it showed heads or tails, one white or on black ball was put into the urn. Balls are drawn
from this urn one at a time, 10 times in
succession (with replacements) and every one turns out to be white. The
chance that the urn contains nothing but white balls is ( frac{1}{2^{k}} . ) Find the value of ( k )
12
1562A biased com wih probatnity ( mathrm{p}, 0<mathrm{p}<1 ) of heads is tossed until a head appears
for the first time. If the probatory that the number of tosses required is even is ( 2 / 5 ) find the value of ( p )
12
1563If the probability of India winning a particular hockey match is ( 0.81 . ) What is the probability of India losing that match?
A . 0.19
B. 0.29
c. 0.59
D. 0.49
12
1564Three unbiased coins are tossed
together. Find the probability of getting
1. Two heads.
2. At least two heads.
3. No heads
12
1565If ( P(A)=0.4, P(B)=0.3 ) and
( P(B / A)=0.5, ) find ( P(A cap B) ) and
( P(A / B) )
12
1566An urn contains 5 red and 2 black balls.
Two balls are randomly drawn. Let ( boldsymbol{X} ) represent the number of black balls. What are the possible values of ( X ? ) Is
( X ) a random variable ?
( mathbf{A} cdot 0,1,2 )
в. 3,5,7
c. 7,7,8
D. 1,5,7
12
1567Ar a selection, the probability of
selection of ( A ) is ( frac{1}{7} ) and that of 8 is ( frac{1}{5} . ) If ( A )
and ( B ) are independent events, then the
probability that neither of them would
be selected is ?
12
1568Which of the following is an example of
a random experiment?
This question has multiple correct options
A. Selecting a card from a pack of playing cards.
B. Measuring the weight of a person.
C. Finding the length of your pencil box.
D. Throwing two coins together.
12
1569A box contains 1 red and 3 identica
white balls. Two balls are drawn at
random in succession without
replacement. Write the sample space for this experiment.
12
1570One of the two events must happen. Given that the chance of one is two-
third of the other, find the odds in favour of the other.
12
1571In a non-leap year the probability of
getting 53 Sundays or 53 Tuesdays or
53 Thursdays is.
A ( cdot frac{1}{7} )
B. ( frac{2}{7} )
( c cdot frac{3}{7} )
D. ( frac{4}{7} )
12
1572A bag contains 15 red, 8 blue and
several green marbles. A marble is selected at random. The probability of drawing a blue marble is ( frac{1}{5} )
5 green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing
a green marble
A ( cdot frac{3}{10} )
В. ( frac{12}{35} )
c. ( frac{23}{40} )
D. ( frac{17}{35} )
12
1573The sum of 5 digit numbers such that the sum of their digit is even is :
( mathbf{A} .50000 )
B. 45000
c. 60000
( D cdot ) none
12
1574Identify the experiment for the
statement “Toss a coin to get head or
tail”.
A. Tossing a coin
B. Rolling of a dice
c. Throw a die
D. Pick a card
12
1575A bag contains 4 white, 5 red and 6 black balls. Three are drawn at random.
Find the probability that (i) no ball drawn is black, (ii) exactly 2 are black
(iii) all are of the same colour.
A ( cdot frac{12}{65}, frac{27}{91}, frac{6}{91} )
В. ( frac{12}{65}, frac{27}{91}, frac{24}{455} )
c. ( frac{12}{65}, frac{27}{91}, frac{14}{455} )
D. ( frac{12}{65}, frac{27}{91}, frac{34}{455} )
12
1576If ( A ) and ( B ) are two mutually exclusive
events such that ( P(A)=0.55 ) and
( P(B)=0.35 ) then ( P(bar{A} cup bar{B})= )
A ( cdot frac{1}{4} )
B.
( c )
D.
12
1577Given a circle of radius ( R ), the
experiment is to randomly select a chord in that circle. Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these
12
1578An urn contains 5 red and 5 black balls
A ball is drawn at random, its colour is noted and is returned to the urn.
Moreover, 2 additional balls of the
colour drawn are put in the urn and then a ball is drawn at random. What is the
probability that the second ball is red?
12
1579When a die is thrown, list the outcomes
of an event of getting:
a number lesser than 5
A .1,2,3,4
B. 1,2,3
c. 3,4,5
D. 4,5
12
1580If ( r cdot v cdot X sim Bleft(n=5, P=frac{1}{3}right), ) then
( P(2<X<4)=ldots . )
A. ( frac{80}{243} )
B. ( frac{40}{243} )
c. ( frac{40}{343} )
D. ( frac{80}{343} )
12
1581For the three events ( A, B & C ) probability of exactly one of the events ( A ) or ( B ) occurs ( = ) probability of exactly one of the events ( C ) or ( A ) occurs ( =p & P )
(all the three events occur
simultaneously) ( =p^{2}, ) where
A ( cdot frac{3 p+2 p^{2}}{2} )
в. ( frac{p+3 p^{2}}{4} )
c. ( frac{p+3 p^{2}}{2} )
D. ( frac{3 p+2 p^{2}}{4} )
12
1582Two bad eggs are accidentally mixed up with ten good ones. Find the probability of picking good eggs.12
1583Given that the events ( A ) and ( B ) are such
( operatorname{that} boldsymbol{P}(boldsymbol{A})=frac{1}{2}, boldsymbol{P}(boldsymbol{A} cup boldsymbol{B})=frac{boldsymbol{3}}{mathbf{5}} ) and
( boldsymbol{P}(boldsymbol{B})=boldsymbol{p} . ) Find ( boldsymbol{p} ) if they are (i)
mutually exclusive (ii) independent.
A . 0.5,0.6
в. 0.1,0.2
c. 0,2,0.4
D. 0.1,0.6
12
1584A boy contains 100 bolts and 50 nuts. It
is given that ( 50 % ) bolts and ( 50 % ) nuts
are rusted. Two objects are selected from the box at random. Find the
probability that both are bolts or both are rusted.
12
1585A pair of dice is thrown 4 times. If
getting a total of 9 in a single throw is considered as a success then find the
mean and variance of successes.
12
1586One card is drawn at random from a
pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A ( cdot frac{1}{13} )
в. ( frac{2}{13} )
c. ( frac{3}{13} )
D. ( frac{4}{13} )
12
1587A purse contains four coins each of
which is either a rupee or two rupees coin. Find the expected value of a coin in
that purse.
12
1588Out of 35 students participating in a debate 10 are girls The probability that the winner is a boy will be
A ( cdot frac{3}{7} )
B.
c. ( frac{1}{7} )
D. ( frac{2}{7} )
12
1589If ( mathbf{a} in[-mathbf{1 0}, mathbf{0}] ) then the probability that
the graph of the function ( mathbf{y}=mathbf{x}^{2}+ )
( 2(a+3) x-(2 a+3) ) is strictly above ( x )
axis is
A ( cdot frac{3}{5} )
B. ( frac{2}{5} )
( c cdot frac{1}{5} )
D. ( frac{4}{5} )
12
1590A pair of dice is thrown 4 times, then the
probability of getting doublets at least twice is
A ( cdot frac{19}{44} )
в. ( frac{21}{44} )
( c cdot frac{31}{44} )
D. ( frac{39}{44} )
12
1591Exactly 6 on each of 3 successive throws
A ( cdot frac{5^{3}}{16^{3}} )
в. ( frac{5}{16^{3}} )
c. ( frac{5^{2}}{16^{3}} )
D. ( frac{1}{16^{3}} )
12
1592In a single throw of a die, the probability of getting a multiple of 3 is
A ( cdot frac{1}{2} )
B. ( frac{1}{3} )
( c cdot frac{1}{6} )
D. ( frac{3}{4} )
12
1593For any two events ( A ) and ( B )
( mathbf{A} cdot P(A)+P(B)>P(A cap B) )
B ( cdot P(A)+P(B)<P(A cap B) )
( mathbf{c} cdot P(A)+P(B) geq P(A cap B) )
D ( . P(A)+P(B) leq P(A cap B) )
12
1594Two cards are drawn simultaneously
(without replacement) from a well-
shuffled pack of 52 cards. Find the
mean and variance of the number of red
cards.
( mathbf{A} cdot ) Mean ( =0.1 ) and Variance ( =0.7 )
B. Mean ( =0.6 ) and Variance ( =0.3 )
C . Mean ( =0.49 ) and Variance ( =0.37 )
D. Mean ( =0 ) and Variance ( =0.45 )
12
1595If the probability of selecting a bolt from
400 bolts is ( 0.1, ) then the mean for the
distribution is
A . 0.09
B . 40
( c .36 )
D. 360
12
1596When a die is thrown, list the outcomes
of an event of getting prime number.
A ( cdot{2,3,5} )
в. {2,4,6}
D. {1,3,5}
12
1597A dice is thrown once,what is the
probability of getting an even prime number.
A ( cdot frac{1}{2} )
B. ( frac{2}{3} )
( c cdot frac{1}{4} )
D.
12
1598is an action where the result
is uncertain.
A. Space
B. Sample
c. Experiment
D. Event
12
1599A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
12
1600The odds against A solving a problem are 8 to 6 and the odds in favour of ( B )
solving the same problem 14 to ( 12 . ) The probability of solving the problem if they both try independently is
A ( cdot frac{67}{91} )
в. ( frac{5}{21} )
c. ( frac{4}{21} )
D.
12
1601u) 0/3 (b) 3/8 (c) 4/5
tu)
The mean and variance of a random varie
al distribution are 4 and 2 respectively, then
e of a random variable X having
is
120031
th
12
1602Which of the following is true regarding law of total probability?
A. It is a fundamental rule relating marginal probabilities to conditional probabilitities.
B. It expresses the total probability of an outcome which can be realized via several distinct events
c. Both are correct
D. None of these
12
1603The sum of the probabilities of each
outcome in an experiment is
12
1604Three coins are tossed. Describe two
events ( A ) and ( B ) which are not mutually
exclusive.
12
1605What is the probability that the wheel
stops at red or pink?
( mathbf{A} )
( B )
6
( c cdot 3 )
D. None of these
12
1606The probability of an event can be
greater than:
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
( D )
12
1607The mean of the numbers obtained on
throwing a die having written 1 on three faces, 2 on two faces and 5 on one face
is:
A .
B. 2
c. 5
D. ( frac{8}{3} )
12
1608( ln ) a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is ( 1 / 3 & ) the probability that he copies the answer is ( 1 / 6 . ) The probability that his answer is correct given that he copied it, is ( 1 / 8 . ) Find the probability that he knew the answer to the question given that he correctly answered it. If expressed in the form of ( a / b ) (simplest form), ( b-a=? )12
1609A car is parked among ( N ) cars standing
in a row, but not at either end. On his
return, the owner finds that exactly ( r ) of
the ( N ) places are still occupied. What is
the probability that both the places neighboring his car are empty?
A ( . ) Required probability ( =frac{(N-r)(N-r-2)}{(N-1)(N-2)} )
B. Required probability ( =frac{(N-r)(N-r-1)}{(N-1)(N-2)} )
c. Required probability ( =frac{(N-r-2)(N-r-1)}{(N-1)(N-2)} )
D. none of these
12
1610If ( P(A)=frac{1}{4}, P(bar{B})=frac{1}{2} ) and ( P(A cup )
B) ( =frac{5}{9}, ) then ( P(A / B) ) is
( ^{A} cdot frac{7}{36} )
в.
c. ( frac{7}{18} )
D. ( frac{7}{72} )
12
1611A die is thrown. Find the probability of getting a prime number.12
1612Two coins are tossed 1000 times and
the outcomes are recorded as below:
( mathbf{2} ) No of heads ( mathbf{0} )
250 Frequency ( 200 quad 550 )
Based on this information, the probability for at most one head is ( frac{a}{b} )
Where ( (a, b)=1, ) then
A ( cdot frac{1}{5} )
в.
( c cdot frac{4}{5} )
D.
12
1613Find the number of numbers of 5 digits that can be formed with the digits
0,1,2,3,4 if the digits can be repeated
in the same number.
12
1614Let A, B, C be three mutually independent events.
Consider the two statements S, and S2
S: A and B u C are independent
S: A and B C are independent
Then,
(1994)
(a) Both S, and S, are true
(b) Only S, is true
(C) Only S, is true
(d) Neither S, nor S, is true
12
1615If ( A ) and ( B ) mutually exclusive events associated with a random experiment such that ( boldsymbol{P}(boldsymbol{A})=mathbf{0 . 4} ) and ( boldsymbol{P}(boldsymbol{B})=mathbf{0 . 5} )
then find ( boldsymbol{P}(overline{boldsymbol{A}} cap overline{boldsymbol{B}}) )
12
161615.
The probabilities that a student passes in Mathematics,
Physics and Chemistry are m,p and c, respectively. Of these
subjects, the student has a 75% chance of passing in at
least one, a 50% chance of passing in at least two, and a
40% chance of passing in exactly two. Which of the following
relations are true?
(1999 – 3 Marks)
(a) p+m+c= 19/20 (b) p+m+c=27/20
(c) pmc=1/10
(d) pmc=1/4
11
1617A die is thrown. Find the probability of getting an odd number12

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