(a) 5/12 (b) 7/12 (c) 3/4 (d) none
24. The chance of getting a sum of 10 in a single throw with two dice is
(a) 10/36 (b) 1/12 (c) 5/36 (d) none
25. The chance of getting a sum of 6 in a single throw with two dice is
(a) 3/36 (b) 4/36 (c) 6/36 (d) 5/36
26. P (B/A) defines the probability that event B occurs on the assumption that A has happened
(a) Yes (b) no (c) both (d) none
27. The complete group of all possible outcomes of a random experiment given an ________
set of events.
(a) mutually exclusive (b) exhaustive (c) both (d) none
28. When the event is ‘certain’ the probability of it is
(a) 0 (b) 1/2 (c) 1 (d) none
29. The classical definition of probability is based on the feasibility at subdividing the possible
outcomes of the experiments into
(a) mutually exclusive and exhaustive
(b) mutually exclusive and equally likely
(c) exhaustive and equally likely
(d) mutually exclusive,exhaustive and equally likely cases.
30. Two unbiased coins are tossed. The probability of obtaining ‘both heads’ is
(a) ¼ (b) 2/4 (c) ¾ (d) none
31. Two unbiased coins are tossed. The probability of obtaining one head and one tail is
(a) ¼ (b) 2/4 (c) ¾ (d) none
32. Two unbiased coins are tossed. The probability of obtaining both tail is
(a) 2/4 (b) 3/4 (c) ¼ (d) none
33. Two unbiased coins are tossed. The probability of obtaining at least one head is
(a) ¼ (b) 2/4 (c) ¾ (d) none
34. When unbiased coins are tossed. The probability of obtaining 3 heads is
(a) 2/4 (b) ¼ (c) ¾ (d) 0
35. When unbiased coins are tossed. The probability of obtaining not more than 3 heads is
(a) ¾ (b) ½ (c) 1 (d) 0
36. When unbiased coins are tossed. The probability of getting both heads or both tails is
(a) ½ (b) ¾ (c) ¼ (d) none
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37. Two dice with face marked 1, 2, 3, 4, 5, 6 are thrown simultaneously and the points on the
dice are multiplied together. The probability that product is 12 is
(a) 4/36 (b) 5/36 (c) 12/36 (d) none
38. A bag contain 6 white and 5 black balls. One ball is drawn. The probability that it is white
is
(a) 5/11 (b) 1 (c) 6/11 (d) 1/11
39. Probability of occurrence of at least one of the events A and B is denoted by
(a) P(AB) (b) P(A+B) (c) P(A/B) (d) none
40. Probability of occurrence of A as well as B is denoted by
(a) P(AB) (b) P(A+B) (c) P(A/B) (d) none
41. Which of the following relation is true ?
(a) P(A)– P(AC)= 1 (b) P(A)+ P(AC)= 1 (c) P(A) P(AC)= 1 (d) none
42. If events A and B are mutually exclusive, the probability that either A or B occurs is given
by
(a) P (A+B)= P(A)– P(B) (b) P (A+B)(A)+ P(B)– P(AB)
(c) P (A+B)= P(A)– P(B)+ P(AB) (d) P (A+B)= P(A)+ P(B)
43. The probability of occurrence of at least one of the 2 events A and B (which may not be
mutually exclusive) is given by
(a) P(A+B)= P(A)– P(B) (b) P(A+B)= P(A)+ P(B)– P(AB)
(c) P(A+B)= P(A)– P(B)+ P(AB) (d) P(A+B)= P(A+B)= P(A)+P (B)
44. If events A and B are independent, the probability of occurrence of A as well as B is given
by
(a) P(AB)= P(A/B) (b) P(AB)= P(A)P(B)
(c) P(AB)= P(A)P(B) (d) None
45. For the condition P(AB)= P(A)P(B)two events A and B are said to be
(a) dependent (b) independent (c) equally like (d) none
46. The conditional probability of an event B on the assumption that another event A has
actually occurred is given by
(a) P(B/ )= P(AB)/P(A) (b) P(A/ )= P(AB)/ P(B)
A B
(c) P(B/ )= P(AB) (d) P(A/ )= P(AB)/ P(A)P(B)
A B
47. Given P(A)= 1 , P(B)= 1 , P(AB)= 1 , the value of P(A+B)is 23 4
a) 3 b) 7 c) 5 d) 1 4 12 6 6
48. Given P(A)= 1 , P(B)= 1 , P (AB)= 1 , the value of P (A/B)is 2 3 4
(a) 1 (b) 1 (c) 2 (d) 3 2 6 3 4
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49. If P (A)= 1, P(B)= 1, the events A & B are 3 4
a) not equally likely b) mutually exclusive
c) equally likely d) none
50. If events A and B are independent then
a) AC and BC are dependent b) AC and B are dependent
c) A and BC are dependent d) AC and BC are also independent
51. A card is drown from each of two well-shuffled packs of cards.The probability that at
least one of them is an ace is
a) 1 b) 25 c) 2 d) none 169 169 13
52. When a die is tossed, the sample space is
a) S =(1,2,3,4,5) b) S =(1,2,3,4) c) S =(1,2,3,4,5,6) d) none
53. If P (A)= 1, P(B)= 2, P (A+B)= 1 then P(AB)is equal to 4 52
a) 3 b) 2 c) 13 d) 3 4 20 20 20
54. If events A and B are independent and P(A)= 2/3 , P(B)= 3/5 then P(A+B)is equal to
13 6 1
a) b) c) d) none
15 15 15
55. The expected no. of head in 100 tosses of an unbiased coin is
a) 100 b) 50 c) 25 d) none
56. A and B are two events such that P(A)= 1/ , P(B) = ¼, P(A+B)= 1/ , than P(B/ ) is equal
3 2 A
to
a) ¼ b) 1/ c) 1/ d) none
3 2
57. Probability mass function is always
a) 0 b) greater than 0
c) greater than equal to 0 d) less than 0
58. The sum of probability mass function is equal to
a) –1 b) 0 c) 1 d) none
59. When X is a continues function f(x)is called
a) probability mass function b) probability density function
c) both d) none
60. Which of the following set of function define a probability space on S = a , a , a
1 2 3
a) P(a )= 1/ , P(a ) = ½, P(a )= ¼ b) P(a )= 1/ , P(a )= 1/ ,P(a )= 1/
1 3 2 3 1 3 2 6 3 2
c) P(a )= P(a )= 2/ , P(a )= ¼ d) None
1 2 3 3
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61. If P (a )= 0, P(a )= 1/ , P (a ) = 2/ then S = a , a , a is a probability space
1 2 3 3 3 1 2 3
a) true b) false c) both d) none
62. If two events are independent then
a) P(B/ )= P(AB) P(A) b) P(B/ )= P(AB) P(B)
A A
c) P(B/ )= P(B) d) P(B/ )P(A)
A A
63. When expected value is negative the result is
a) favourable b) unfavourable
c) both d) none to the player
64. The expected value of X, the sum of the scores, when two dice are rolled is
a) 9 b) 8 c) 6 d) 7
65. Let A and B be the events with P(A)= 1/ , P(B) = ¼ and P(AB)= 1/ then P(A/ ) is equal
3 12 B
to
a) 1/ b) ¼ c) ¾ d) 2/
3 3
66. Let A and B be the events with P(A)= 2/ , P(B)= ¼ and P(AB)= 1/ then P(B/ ) is equal to
3 12 A
a) 7/ b) 1/ c) 1/ d) none
8 3 8
67. The odds in favour of one student passing a test are 3:7. The odds against another student
passing at are 3:5. The probability that both pass is
a) 7/ b) 21/ c) 9/ d) 3/
16 80 80 16
68. The odds in favour of one student passing a test are 3:7. The odds against another student
passing at are 3:5. The probability that both fail is
a) 7/ b) 21/ c) 9/ d) 3/
16 80 80 16
69. In formula P(B/ ), P(A) is
A
a) greater than zero b) less than zero
c) equal to zero d) greater than equal to zero
70. Two events A and B are mutually exclusive means they are
a) not disjoint b) disjoint c) equally likely d) none
71. A bag contains 10 white and 10 black balls A ball is drawn from it. The probability that it
will be white is
(a) 1/10 (b) 1 (c) ½ (d) none
72. Two dice are thrown at a time. The probability that the nos shown are equal is
(a) 2/6 (b) 5/6 (c) 1/6 (d) none
73. Two dice are thrown at a time. The probability that ‘the difference of nos shown is 1’ is
(a) 11/18 (b) 5/18 (c) 7/18 (d) none
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74. Two dice are thrown together. The probability that ‘the event the difference of nos shown
is 2’ is
(a) 2/9 (b) 5/9 (c) 4/9 (d) 7/9
75. The probability space in tossing two coins is
(a) {(H,H), (H,T), (T,H)} (b) {(H,T),(T,H),(T,T)}
(c) {(H,H), (H,T), (T.H), (T,T)} (d) none
76. The probability of drawing a white ball from a bag containing 3 white and 8 balls is
(a) 3/5 (b) 3/11 (c) 8/11 (d) none
77. Two dice are thrown together. The probability of the event that the sum of nos. shown is
greater than 5 is
(a) 13/18 (b) 15/18 (c) 1 (d) none
78. A traffic census show that out of 1000 vehicles passing a junction point on a highway 600
turned to the right. The probability of an automobile turning the right is
(a) 2/5 (b) 3/5 (c) 4/5 (d) none
79. Three coins are tossed together. The probability of getting three tails is
(a) 5/8 (b) 3/8 (c) 1/8 (d) none
80. Three coins are tossed together.The probability of getting exactly two heads is
(a) 5/8 (b) 3/8 (c) 1/8 (d) none
81. Three coins are tossed together. The probability of getting at least two heads is
(a) 1/2 (b) 3/8 (c) 1/8 (d) none
82. 4 coins are tossed. The probability that there are 2 heads is
(a) 1/2 (b) 3/8 (c) 1/8 (d) none
83. If 4 coins are tossed. The chance that there should be two tails is
(a) 1/2 (b) 3/8 (c) 1/8 (d) none
84. If A is an event and AC its complementary event then
(a) P(A)=P(AC)–1 (b) P(AC)=1–P(A) (c) P(A)=1 + P(AC) (d) none
85. If P(A)= 3/8, P(B)= 1/3 and P(AB)= ¼ then P(AC) is equal to
(a) 5/8 (b) 3/8 (c) 1/8 (d) none
86. If P(A)= 3/8, P(B)= 1/3 then P(A) is equal to
(a) 1 (b) 1/3 (c) 2/3 (d) none
87. If P(A)= 3/8, P(B)= 1/3 and P(AB)= ¼ then P(A + B)is
(a) 13/24 (b) 11/24 (c) 17/24 (d) none
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(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:4)(cid:6)(cid:7)(cid:6)(cid:8)(cid:9)(cid:10)(cid:5)(cid:11)(cid:12)(cid:10)(cid:13)(cid:14)(cid:1)(cid:13)(cid:15)(cid:8)(cid:13)(cid:12)(cid:10)(cid:16)(cid:5)(cid:7)(cid:17)(cid:13)(cid:10)(cid:4)(cid:9)(cid:10)(cid:18)(cid:5)(cid:8)(cid:19)(cid:13)(cid:18)(cid:5)(cid:8)(cid:6)(cid:15)(cid:5)(cid:7)(cid:10)(cid:13)(cid:14)(cid:1)(cid:13)(cid:15)(cid:8)(cid:5)(cid:8)(cid:6)(cid:3)(cid:11)
88. If P(A)= 1/5, P(B)= 1/2 and A and B are mutually exclusive then P(AB) is
(a) 7/10 (b) 3/10 (c) 1/5 (d) none
89. The probability of throwing more than 4 in a single throw from an ordinary die is
(a) 2/3 (b) 1/3 (c) 1 (d) none
90. The probability that a card drawn at random from the pack of playing cards may be
either a queen or an ace is
(a) 2/13 (b) 11/13 (c) 9/13 (d) none
91. The chance of getting 7 or 11 in a throw of 2 dice is
(a) 7/9 (b) 5/9 (c) 2/9 (d) none
92. If the probability of a horse A winning a race is 1/6 and the probability of a horse B
winning the same race is 1/4 , what is the probability that one of the horses will win
(a) 5/12 (b) 7/12 (c) 1/12 (d) none
93. If the probability of a horse A winning a race is 1/6 and the probability of a horse B
winning the same race is 1/4 , What is the probability that none of them will win
(a) 5/12 (b) 7/12 (c) 1/12 (d) none
94. If P (A)= 7/8 then(P(AC) is equal to
(a) 1 (b) 0 (c) 7/8 (d) 1/8
95. The value of P(S) were S is the sample space is
(a) –1 (b) 0 (c) 1 (d) none
96. A man can kill a bird once in three shots.The probabilities that a bird is not killed is
(a) 1/3 (b) 2/3 (c) 1 (d) 0
97. If on an average 9 shops out of 10 return safely to a port. The probability of one ship
returns safely is
(a) 1/10 (b) 8/10 (c) 9/10 (d) none
98. If on an average 9 shops out of 10 return safely to a port. The probability of one ship does
not reach safely is
(a) 1/10 (b) 8/10 (c) 9/10 (d) none
99. The probability of winning of a person is 6/11 and at a result he gets Rs.77/= .The
expectation of this person is
(a) Rs.35/= (b) Rs.42/= (c) Rs.58/= (d) none
100.A family has 2 children. The probability that both of them are boys if it is known that one
of them is a boy
(a) 1 (b) 1/2 (c) 3/4 (d) none
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101.The Probability of the occurrence of a no. greater then 2 in a throw of a die if it is known
that only even nos. can occur is
(a) 1/3 (b) 1/2 (c) 2/3 (d) none
102.A player has 7 cards in hand of which 5 are red and of these five 2 are kings. A card is
drawn at random. The probability that it is a king, it being known that it is red is
(a) 2/5 (b) 3/5 (c) 4/5 (d) none
103.In a class 40 % students read Mathematics, 25% Biology and 15 % both Mathematics and
Biology. One student is select at random. The probability that he reads Mathematics if it is
known that he reads Biology is
(a) 2/5 (b) 3/5 (c) 4/5 (d) none
104.In a class 40 % students read Mathematics, 25% Biology and 15% both Mathematics and
Biology. One student is select at random.The probability that he reads Biology if he reads
Mathematics
(a) 7/8 (b) 1/8 (c) 3/8 (d) none
105.Probability of throwing an odd no with an ordinary six faced die is
(a) 1/2 (b) 1 (c) –1/2 (d) 0
106.For a certain event A ,P (A) is equal to
(a) 1 (b) 0 (c) –1 (d) none
107.When none of the outcomes is favourable to the event then the event is said to be
(a) certain (b) sample (c) impossible (d) none
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AAAAANNNNNSSSSSWWWWWEEEEERRRRRSSSSS
1 (b) 2 (d) 3 (a) 4 (b) 5 (b)
6 (a) 7 (c) 8 (a) 9 (b) 10 (b)
11 (b) 12 (a) 13 (b) 14 (c) 15 (d)
16 (d) 17 (a) 18 (a) 19 (d) 20 (c)
21 (d) 22 (b) 23 (a) 24 (b) 25 (d)
26 (a) 27 (b) 28 (c) 29 (d) 30 (a)
31 (b) 32 (c) 33 (c) 34 (d) 35 (c)
36 (a) 37 (a) 38 (c) 39 (b) 40 (a)
41 (b) 42 (d) 43 (b) 44 (c) 45 (b)
46 (a) 47 (b) 48 (d) 49 (a) 50 (d)
51 (b) 52 (c) 53 (d) 54 (a) 55 (b)
56 (a) 57 (c) 58 (c) 59 (b) 60 (b)
61 (a) 62 (c) 63 (b) 64 (d) 65 (a)
66 (c) 67 (d) 68 (b) 69 (a) 70 (b)
71 (c) 72 (c) 73 (b) 74 (a) 75 (c)
76 (b) 77 (a) 78 (b) 79 (c) 80 (b)
81 (a) 82 (b) 83 (b) 84 (b) 85 (a)
86 (c) 87 (b) 88 (a) 89 (b) 90 (a)
91 (c) 92 (a) 93 (b) 94 (d) 95 (c)
96 (b) 97 (c) 98 (a) 99 (b) 100 (b)
101 (c) 102 (a) 103 (b) 104 (c) 105 (a)
106 (a) 107 (c)
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