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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. 6 coins are tossed simultaneously. The propability of getting atleast 6 heads is :
(A)
(B)
(C)
(D)
2. The probabilities of three mutually
exclusive events are
The statement is : (A) True (B) Wrong (C) Could be either (D) Do not know
3. A & B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is :
(A)
(B)
(C)
(D)
4. A & B are two events such that and P (A) = 0.4, P (A + B) = 0.7 and P (AB) = 0.2, then P (B) = (A) 0.1 (B) 0. (C) 0.5 (D) None of these 5. Suppose that A, B, C are events such
that P (A) = P (B) = P (C) =
P (AB) = P (CB) = 0, P (AC) =
then P (A + B) = (A) 0.125 (B) 0. (C) 0.375 (D) 0.
6. A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is :
(A)
(B)
(C)
(D) 0
7. If A & B are two events such that, P (A ∪ B) = P (A ∩ B), then the true relation is : (A) P (A) = P (B) = 0
(B) P (A) + P (B) = P (A) P
B
A
(C) P (A) + P (B) = 2 P (A) P
B
A
^
(D) None of these
8. A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is :
(A)
(B)
(C)
(D) 1
9. A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is :
(A)
(B)
(C)
(D)
10. The probability of happening an even A is 0.5 and that of B is 0.3. If A & B are mutually exclusive events, then
Probability
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
the probability of happening neither A nor B is : (A) 0.6 (B) 0. (C) 0.21 (D) None of these
11. If P (A) = 0.4, P (B) = x, P (A ∪ B) = 0.7 and the events A & B are independent, then x =
(A)
(B)
(C)
(D) None of these
12. A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail.
(A)
(B)
(C)
(D)
13. A man draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues this process until he gets a card of spade. The probability that he will fail the first two times is :
(A)
(B)
(C)
(D) None of these
14. In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before
making the second selection. The probability that both the bulbs are without defect is :
(A)
(B)
(C)
(D)
15. If A & B are any two events, then the true relation is : (A) P (A ∩ B) > P (A) + P (B) - 1 (B) P (A ∩ B) < P (A) + P (B) (C) P (A ∩ B) = P (A) + P (B) − P (A ∪ B) (D) None of these 16. A box contains 15 tickets numbered 1, 2, ..... , 15. Seven tickets are drawn at random one after the other with replacement. The probability that the greatest number on a drawn ticket is 9, is :
(A)
6 ^
^ (B)^
7 ^
(C)
7
(D) None of these
17. A purse contains 4 copper coins & 3 silver coins, the second purse contains 6 copper coins & 2 silver coins. If a coin is drawn out of any purse, then the probability that it is a copper coin, is :
(A)
(B)
(C)
(D) None of these
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
probability that the minimum face value is not less that 2 and the maximum face value is not greater than 5, is :
(A)
(B)
(C)
(D)
28. A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is :
(A)
(B)
(C)
(D)
29. Cards are drawn one by one at random from a well shuffled full pack of 52 cards until two aces are obtained for the first time. If N is the number of cards required to be drawn then Pr (N = n), where 2 ≤ n ≤ 50, is :
(A)
( n − ) ( − n) ( −n) × × ×
(B)
( n − ) ( − n) ( −n) × × ×
(C)
( n − ) ( − n) ( −n) × × ×
(D)
( n − ) ( − n ) ( −n) × × ×
30. The probabilities that A & B will die within a year are p & q respectively, then the probability that only one of
them will be alive at the end of the year is : (A) p + q (B) P + q - 2 qp (C) p + q - pq (D) p + p + pq
31. One 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)
(B)
(C)
(D)
32. The letter of the word “ASSASSIN” are written down at random in a row. The probability that no two S occur together is :
(A)
(B)
(C)
(D) None of these
33. A bag A contains 2 white & 3 red balls & bag B contains 4 white & 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag B was :
(A)
(B)
(C)
(D)
34. India plays two matches each with West Indies & Australia. In any match
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
the probabilities of India getting point 0, 1 & 2 are 0.45, 0.05 & 0. respectively. Assuming that the outcomes are independents, the probability of India getting atleast 7 points is : (A) 0.8750 (B) 0. (C) 0.0625 (D) 0.
35. From the word “POSSESSIVE”, a letter is chosen at random. The probability of it to be S is :
(A)
(B)
(C)
(D)
36. If A & B are two independent events such that P (A ∩ B′) = 3/25 and P (A′ ∩ B) = 8/25, then P (A) =
(A)
(B)
(C)
(D)
37. A fair coin is tossed n times. Let X be the number of times head is observed. If P (X = 4), P (X = 5) and P (X = 6) are in H.P., then it is equal to (A) 7 (B) 10 (C) 14 (D) None of these 38. A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is :
(A)
(B)
(C)
(D) None of these
39. Urn A contains 6 red & 4 black balls and urn B contains 4 red & 6 black balls. One ball is drawn at random from urn A & placed in urn B. Then one ball is drawn at random from urn B & placed in urn A. If one ball is now drawn at random from urn A, the prob. that it is found to be red is :
(A)
(B)
(C)
(D) None of these
40. A box contains 100 tickets numbered 1, 2, ..... , 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability :
(A)
(B)
(C)
(D) None of these
41. If 1 3 3
− p (^) and 1 2 2
− p (^) are the
probabilities of 3 mutually exclusive events, then the set of all values of p is :
(A)
≤ p ≤ (B)
< p<
(C)
≤ p ≤ (D)
< p<
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
49. An 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, ..... , 12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is : (A) 0.24 (B) 0. (C) 0.024 (D) None of these 50. A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is :
(A)
(B)
(C)
(D)
51. Three groups A, B, C are competing for positions on the Board fo Directors of a company. The probabilities of their winning are 0.5, 0.3, 0. respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for the group B & C are 0.6 & 0.5 respectively. The prob. that the new product will be introduced, is : (A) 0.18 (B) 0. (C) 0.10 (D) 0. 52. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target atleast three times, is :
(A)
(B)
(C)
(D)
53. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these 3 vertices is equilateral, is equal to :
(A)
(B)
(C)
(D)
54. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour, is :
(A)
(B)
(C)
(D) None of these
55. In order to get atleast once a head with probability ≥ 0.9, the number of times a coin needs to be tossed, is : (A) 3 (B) 4 (C) 5 (D) None of these 56. Let 0 < P (A) < 1, 0 < P (B) < 1 and P (A ∪ B) = P (A) + P (B) − P (A) P (B). Then :
(A) P
B
A
= P (B) - P (A)
(B) P (Ac^ ∪ Bc) = P (Ac) + P (Bc) (C) P (A ∪ B)c^ = P (Ac) P (Bc)
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(D) P
A
B
= P (A)
57. Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years, is :
(A)
(B)
(C)
(D)
58. A die is tossed thrice. A success is getting a or 6 on a toss. The mean & the variance of number of successes
(A) μ = 1, σ^2 =
(B) μ =
, σ^2 = 1
(C) μ = 2, σ^2 =
(D) None of these
59. In 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)
(B)
(C)
(D)
60. If X follows a binomial distribution with parameters n = 6 & p and 4 (P (X = 4)) = P (X = 2), then p =
(A)
(B)
(C)
(D)
- The value of C for which, P (X = k) = Ck^2 can serve as the prob. function of a random variable X, that takes 0, 1, 2, 3, 4 is :
(A)
(B)
(C)
(D)
62. For the three events A, B & C, P (exactly one of the events A or B occurs = P (exactly one of the events B or C occurs) = P (exactly one of the events C or A occurs) = p & P (all the three events occur simultaneously) =
p^2 , where 0 < p <
. Then the prob.
of atleast one of the three events A, B and C occuring, is :
(A)
p + p^2 (B)
p + 3 p 4
2
(C)
p + 3 p 2
2 (D)
p + p^2
63. A six faced dice is biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is :
(A)
(B)
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