CBSE Class 11 Mathematics Probability Worksheet Set A

Question. The probability that a randomly chosen 5-digit number is made from exactly two digits is : 
(a) 135/10⁴
(b) 121/10⁴
(c) 150/10⁴
(d) 134/10⁴
Answer : A

Question. For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is 4/5, then the probability that he is unable to solve less than two problems is :
(a) 201/5 (1/5)⁴⁹
(b) 316/25 (4/5)⁴⁸
(c) 54/5 (4/5)⁴⁹
(d) 164/25 (1/5)⁴⁸
Answer : C

Question. Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
(a) P(A|B) = P(B) – P(A)
(b) P(A|B) ≥ P(A)
(c) P(A|B) ≤ P(A)
(d) P(A|B) = 1
Answer : B

Question. Let A and B be two independent events such that P(A) = 1/3 and P(B) = 1/6. Then, which of the following is TRUE ? [Jan. 8, 2020 (I)]
(a) P(A/B) = 2/3
(b) P(A/B’) = 1/3
(c) P(A’/B’) = 1/3
(d) P(A/(A È B)) = 1/4
Answer : B

Question. An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value –1. Then the expected value of X, is:
(a) 3/16
(b) 1/8
(c) - 3/16
(d) 1/8
Answer : B

Question. In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 1/4. If the probability that at most two machines will be out of service on the same day is (3/4)4 k, then k is equal to:
(a) 17/8
(b) 17/4
(c) 17/2
(d) 4
Answer : A

Question. Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :
(a) 7/10
(b) 1/2
(c) 2/5
(d) 3/5
Answer : C

Question. Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is: 
(a) 1/11
(b) 1/10
(c) 1/12
(d) 1/17
Answer : A

Question. Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :
(a) 5
(b) 6
(c) 8
(d) 7
Answer : D

Question. Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8 respectively. If all hit at the target independently, then the probability that the target would be hit, is:
(a) 25/192
(b) 7/32
(c) 1/192
(d) 25/32
Answer : D

Question. In 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) 200/6⁵
(b) 150/6⁵
(c) 225/6⁵
(d) 175/6⁵
Answer : D

Question. Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is  
(a) 2/3
(b) 8/17
(c) 4/17
(d) 2/5
Answer : B

Question. In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is :
(a) 9/16
(b) 11/16
(c) 13/16
(d) 15/1 
Answer : B

Question. Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2, then a value of P(E)/P(F) is :
(a) 4/3
(b) 3/2
(c) 1/3
(d) 5/12
Answer : A

Question. Let A, B and C be three events, which are pair-wise independence and E denotes the complement of an event E. If P (A ∩ B ∩ C) = 0 and P (C) > 0, then P[( A ∩ B ) |C] is equal to.
(a) P (A) + P ( B )
(b) P ( A ) – P ( B )
(c) P ( A ) – P (B)
(d) P ( A ) + P ( B )
Answer : C

Question. In a game, a man wins ₹ 100 if he gets 5 or 6 on a throw of a fair die and loses ₹ 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :
(a) (400/9) loss
(b) (0)
(c) (400/3) gain
(d) (400/3) loss
Answer : B

Question. An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is:
(a) 21/49
(b) 27/49
(c) 26/49
(d) 32/49
Answer : D

Question. An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, ..., 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is: 
(a) 13/36
(b) 15/72
(c) 19/72
(d) 19/36
Answer : C

Question. If two different numbers are taken from the set (0, 1, 2, 3, ......., 10), then the probability that their sum as well as absolute difference are both multiple of 4, is :
(a) 7/55
(b) 6/55
(c) 12/55
(d) 14/55
Answer : B

Question. Given two independent events, if the probability that exactly one of them occurs is 26/49 and the probability that none of them occurs is 15/49, then the probability of more probable of the two events is :
(a) 4/7
(b) 6/7
(c) 3/7
(d) 5/7
Answer : A

Please click on below link to download CBSE Class 11 Mathematics Probability Worksheet Set A