CBSE Class 12 Mathematics Probability Worksheet Set 01

Question. Let A and B be the sets {1, 2, …10} and {1, 2, …20} respectively. A function is selected randomly from A to B the probability that the function is non-decreasing is
(a) ²⁹C₁₀/(20)¹⁰
(b) ²⁹C₂₀/(20)¹⁰
(c) ²⁹C₁₉/(20)¹⁰
(d) None of these
Answer : C

Question. Matrices of order 3 × 3 are formed by using the elements of the set A = {–3, –2, –1, 0, 1, 2, 3}, then probability that matrix is either symmetric or skew symmetric is
(a) 1/7⁶ + 1/7³
(b) 1/7⁹ + 1/7³ - 1/7⁶ 
(c) 1/7³ + 1/7⁹
(d) 1/7³ + 1/7⁶ - 1/7⁹
Answer : D

Question. If a ∈[– 20, 0], then probability that the graph of the function y =16x² + 8(a + 5) x – 7a – 5 is strictly above the x-axis is
(a) 7/20
(b) 20/13
(c) 20/17
(d) 3/20
Answer : B

Question. Given that the sum of two non-negative quantities is 200, the probability that their product is not less than 3/4 times their greatest product value is
(a) 7/16
(b) 101/201
(c) 9/16
(d) 10/16
Answer : B

Question. Raj and Sanchita are playing game in which they throw two dice alternately till one of them gets 9. Which one of the following could be the probability that Sanchita win the game?
(a) 7/15 or 8/15
(b) 6/11 or 5/11
(c) 8/17 or 9/17
(d) None of these
Answer : C

Question. If X follows a binomial distribution with parameters n = 8 and p = 1/2, then p(|x – 4| < 2) is equal to
(a) 121/128
(b) 119/128
(c) 117/128
(d) 115/128
Answer : B

Question. Entries of a 2 × 2 determinant are chosen from the set {–1, 1}. The probability that determinant has zero value is
(a) 1/4
(b) 1/3
(c) 1/2
(d) None of these
Answer : C

Question. The odds in favour of a book reviewed by three independent critics are, respectively, 5 : 2, 4 : 3 and 3 : 4. The probability that majority of the critics give favourable remark is
(a) 210/343
(b) 209/343
(c) 211/343
(d) 205/343
Answer : B

Question. In a Competitive test, a candidate guesses, copies or knows the answer to a multiple choice question with four choices. 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 he copied it is 1/8. Find the probability that he knew the answer to the question, given that he answered it correctly.
(a) 24/29
(b) 26/29
(c) 22/29
(d) None of these
Answer : A

Question. A wire of length l is cut into three pieces. Then the probability that the three pieces form a triangle is
(a) 1/2
(b) 1/4
(c) 2/3
(d) None of these
Answer : B

Question. Ravi and Rashmi are each holding 2 red cards and 2 black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi, and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let p be the probability that both have all 4 cards of the same colour. Then p satisfies
(a) p ≤ 5%
(b) 5% < p ≤ 10%
(c) 10% < p ≤ 15%
(d) 15% < p
Answer : A

Question. On each evening a boy either watches DOORDARSHAN channel or TEN SPORTS. The  probability that he watches TEN SPORTS is 4/5.
If he watches DOORDARSHAN, there is a chance of 3/4 that he will be asleep, while it is 1/4 when he watches TEN SPORTS. On one day, the/boy is found to be asleep. The probability that the boy watched DOORDARSHAN is
(a) 5/7
(b) 2/7
(c) 3/7
(d) 4/7
Answer : C

Question. A boy whose hobby is tossing a fair coin is to score one point for every tail and 2 points for every head. The boy goes on tossing the coin, till his score reaches n or exceeds n where n ≥ 2.
If p_n is the probability that his score attains exactly n, then p_n is equal to
(a) pn–1 + p_n–2
(b) (1/2) p_n - 1 + p_n - 2
(c) 2/3 + (-1)ⁿ/2ⁿ
(d) 2ⁿ+1 +(-1)ⁿ/3.2ⁿ
Answer : D

Question. A die is thrown 2n + 1 times, n ∈ N. The probability that faces with even numbers show odd numbers of times, is
(a) 2n+1/4n+3
(b) less than 1/2
(c) greater than 1/2
(d) None of these
Answer : D

Question. A book writer writes a good book with probability 1/2. If it is a good book, the probability that it will be published is 2/3 , otherwise it is 1/4 . If he writes 2 books, the probability that at least one book will be published is
(a) 407/576
(b) 411/576
(c) 405/576
(d) 307/576
Answer : A

Question. Let the probability Pn that a family has exactly n children be apⁿ, when n ≥ 1 and P₀ = 1 – ap (1 + p + p² + ...). Suppose that all sex distributions of n children have the same probability. If k ≥ 1 , then the probability that a family contains exactly k boys is
(a) 2a(2-p)^k+1
(b) p^k(2-p)
(c) 2a-p^k/(2-p)^k+1
(d) None of these
Answer : C

Question. The probability of men getting a certain disease is 1/2 and that of women getting the same disease is 1/5 The blood test that identifies the disease gives the correct result with probability 4/5 Suppose a person is chosen at random from a group of 30 males and 20 females, and the blood test of the person is found to be positive. What is the probability that the chosen person is a man?
(a) 75/107
(b) 3/5
(c) 15/19
(d) 3/10
Answer : A

Numeric Value Answer

Question. A and B play a game of tennis. The situation of the game is as follows : if one scores two consecutive points after a deuce, he wins, if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 3/2 . The game is at deuce and A is serving.
Probability that A will win the match is, (serves are changed after each game).
Answer : (0.50

Question. A special die is so constructed that the probabilities of throwing 1, 2, 3, 4, 5 and 6 are (1 – k) / 6, (1 + 2k) / 6, (1 – k) / 6, (1 + k) / 6, (1 – 2k) / 6 and (1 + k) / 6, respectively. If two such dice are thrown and the probability of  getting a sum equal to 9 lies between 1/9 and 2/9 , then the integral value of k is.
Answer : 0

Question. In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner had succeeded in the first trial, is
Answer : 0.60

Question. The probablilty that the length of a randomly chosen chord of a circle lies between 2/3 and 5/6 of its diameter is
Answer : 0.25

Question. A number x is selected from the set of first 9 natural numbers (i.e., x = 1, 2, 3, ......., 9). If the probability that f(f(x)) = x where f(x) = x² – 3x + 3 is m/9, then m is equal to _________.
Answer : 2

Question. A determinant of the second order is made with the elements 0 and 1. If m/n be the probability that the determinant made is non-negative, where m and n are relative primes, then the value of n – m is
Answer : 3

Question. An artillery target may be either at point I with probability 8/9 or at the point (II) with probability 1/9. There are 21 shells each of which can be fired either at point I or II. Each shell may hit the target independently of the other shell with probability 1/2. Minimum number of shells that must be fired at point I to hit the target with maximum probability is equal to 2k. Then value of k is.
Answer : 6

Question. A sportsman's chance of shooting an animal at a distance r > a ("a" is constant) is given to be a²/r². He fires at r = 2a and if he misses, then again fires at r = 3a. He repeats the same process at r = 4a, 5a and 6a. When he misses at r = 6a, the animal escapes into the jungle. If the odds against the sportsman are p : q, then q – p is _______.,
Answer : 5

Please click on below link to download CBSE Class 12 Mathematics Probability Worksheet Set A