CBSE Class 12 Mathematics Probability Assignment Set 01

Question. In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins.
The probability of A winning the game is :
(a) 5/31
(b) 31/61
(c) 5/6
(d) 30/6 
Answer : D

Question. In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is _________. 
Answer : (11.00)

Question. 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 8, given that the product of these digits is ero, equals:
(a) 1/7
(b) 5/14
(c) 1/50
(d) 1/14
Answer : D

Question. Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals: 
(a) 49/169
(b) 52/169
(c) 24/169
(d) 25/169
Answer : D

Question. The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :
(a) 5
(b) 3
(c) 4
(d) 2
Answer : C

Question. It is given that the events A and B are such that P (A) = 1/4 P (A/B) and P (B) = 2/3 Then P(B) is
(a) 1/6
(b) 1/3
(c) 2/3
(d) 1/2
Answer : B

Question. The probability of a man hitting a target is 1/10 The least number of shots required, so that the probability of his hitting the target at least once is greater than 1/4 is ___________. 
Answer : (3.00)

Question. A 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 ust by guessing is: 
(a) 17/3⁵
(b) 13/3⁵
(c) 11/3⁵
(d) 10/3⁵
Answer : C

Question. A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 2/1, 3/1 and 4/1. Probability that the problem is solved is
(a) 4/3
(b) 2/1
(c) 3/2
(d) 3/1
Answer : A

Question. A random variable X has the following probability distribution:
X      :  1      2     3      4      5
P(X) :  K²   2K    K     2K    5K²
Then, P(X > 2) is equal to: 
(a) 7/12
(b) 1/36
(c) 1/6
(d) 23/36
Answer : D

Question. A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then
(mean of X / standard deviation of X) is equal to:
(a) 4
(b) 4√3
(c) 3√2
(d) 4√3/3
Answer : B

Question. A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is: 
(a) 6/25
(b) 12/5
(c) 6
(d) 4
Answer : B

Question. If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P (X = 3), then E(X), the mean of variable X, is
(a) 2 – p
(b) 3 – p
(c) p/2
(d) p/3
Answer : B

Question. Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______. 
Answer : (11)

Question. An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is : 
(a) 496/729
(b) 192/729
(c) 240/729
(d) 256/729
Answer : D

Question. The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
(a) 256/28
(b) 256/219
(c) 256/128
(d) 256/37
Answer : A

Question. The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is
(a) 4/1
(b) 32/1
(c) 16/1
(d) 8/1
Answer : B

Question. If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is :
(a) 9/16
(b) 3/4
(c) 1/16
(d) 15/16
Answer : D

Question. Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 then p lies in the interval 
(a) (3/4, 11/12]
(b) [0, 1/2]
(c) (11/12, 1]
(d) (1/2, 3/4]
Answer : B

Question. In a binomial distribution B (n, p = 1/4), if the probability of at least one success is greater than or equal to 9/10, then n is greater than:
(a) 1/log₁₀ 4 + log₁₀3
(b) 9/log₁₀ 4 - log₁₀3
(c) 4/log₁₀ 4 + log₁₀3
(d) 1/log₁₀ 4 - log₁₀3
Answer : D

Question. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
(a) 8/729
(b) 8/243
(c) 1/729
(d) 8/9.
Answer : B

Question. At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals.
The probability that there is at the most one phone call during a 10-minute time period is
(a) 6/5^e
(b) 6/5
(c) 55/6
(d) 6/e⁵
Answer : D

Question. A random variable X has Poisson distribution with mean 2.
Then P (X > 1.5) equals
(a) 2/e²
(b) 0
(c) 1- 3/e²
(d) 3/e²
Answer : C

Question. A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is
(a) 8/3
(b) 3/8
(c) 4/5
(d) 5/4
Answer : D

Case Based Questions

1. A coach is training 3 players. He observes that the player A can hit a target 4 times in 5 shots, player B can hit 3 times in 4 shots and the player C can hit 2 times in 3 shots.
From the situation, answer the following.

Question. Let the target is hit by A, B: the target is hit by B and C: the target is hit by A and C. Then, the probability that A, B and C all will hit, is
(a) 4/5
(b) 3/5
(c) 2/5
(d) 1/5

Answer : C

Question. Referring to (i), what is the probability that B, C will hit and A will lose?
(a) 1/10
(b) 3/10
(c) 7/10
(d) 4/10

Answer : A

Question. With reference to the events mentioned in (i), what is the probability that any two of A, B and C will hit?
(a) 1/30
(b) 11/30
(c) 17/30
(d) 13/30

Answer : D

Question. What is the probability that 'none of them will hit the targets?
(a) 1/30
(b) 1/60
(c) 1/15
(d) 2/15

Answer : B

Question. What is the probability that at least one of A, B or C will hit the target's?
(a) 59/60
(b) 2/5
(c) 3/5
(d) 1/60

Answer : A

2. In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/3. Let E₁, E₂, E be the events that the student knows the answer guesses the answer and answers correctly respectively.

Based on the above information, answer the following.

Question. What is the value of P(E₁)?
(a) 2/5
(b) 1/3
(c) 1
(d) 3/5

Answer : D

Question. Value of P(E | E₁) is
(a) 1/3
(b) 1
(c) 2/3
(d) 415

Answer : A

Question. What is the probability that the student knows the answer it correctly?
(a) 2/11
(b) 5/3
(c) 9/11
(d) 13/3

Answer : C

3. In an office, three employees Vinay, Sonia and Iqbal process incoming copies of a certain form. Vinay process 50% of the forms. Sonia processes 20% and Iqbal the remaining 30% of the forms. Vinay has an error rate of 0.06, Sonia has an error rate of 0.04 and Iqbal has an error rate of 0.03.

Based on the above information answer the following:

Question. The conditional probability that an error is committed in processing given that Sonia processed the form is:
(a) 0.0210
(b) 0.04
(c) 0.47
(d) 0.06

Answer : B

Question. The probability that Sonia processed the form and committed an error is:
(a) 0.005
(b) 0.006
(c) 0.008
(d) 0.68

Answer : C

Question. The total probability of committing an error in processing the form is
(a) 0
(b) 0.047
(c) 0.234
(d) 1

Answer : B

Question. The manager of the company wants to do a quality check. During the inspection, he selects a form at random from the days’ output of processed forms. If the form selected at random has an error, the probability that the form is NOT processed by Vinay is:
(a) 1
(b) 30/47
(c) 17/47
(d) 30/37

Answer : C

Question. The probability that Iqbal processed the form and committed an error is:
(a) 0.009
(b) 0.006
(c) 0.008
(d) 0.68

Answer : A

4. A shopkeeper sells three types of flower seeds A₁, A₂, and A₃. They are sold as a mixture where the proportions are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively.

Based on the above information answer the following questions:

Question. The probability of a randomly chosen seed to germinate:
(a) 0.69
(b) 0.39
(c) 0.49
(d) 0.59

Answer : C

Question. The probability that the seed will not germinate given that the seed is of type A3:
(a) 15/100
(b) 65/100
(c) 75/100
(d) 55/100

Answer : B

Question. The probability that the seed is of the type A2 given that a randomly chosen seed does not germinate.
(a) 22/51
(b) 55/51
(c) 51/16
(d) 16/51

Answer : D

Question. The probability that it is of the type A1 given that a randomly chosen seed does not germinate is:
(a) 22/51
(b) 5/51
(c) 1/16
(d) 16/51

Answer : A

Question. The probability that it will not germinate given that the seed is of type A1
(a) 55/100
(b) 65/100
(c) 35/100
(d) 45/100

Answer : A

Click on link below to download CBSE Class 12 Mathematics Probability Assignment Set A