Please refer to the MCQ Questions for Class 12 Mathematics Chapter 13 Probability with Answers. The following Probability Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Probability Class 12 MCQ Questions with Answers

See below Probability Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question.****In a college, 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is**

(a) 1/10

(b) 2/5

(c) 9/20

(d) 1/3

**Answer**

B

**Question. A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag. What is the probability that none is marked with the digit 0?**

(a) (9/10)^{2}

(b) (9/10)^{3}

(c) (9/10)^{4}

(d) (9/10)^{5 }

## Answer

D

**Question. A pair of dice is thrown 4 times. If getting a doublet is considered a success, the probability of two successes is**

(a) 25/ 128

(b) 13 /216

(c) 25 /216

(d) 11 /128

## Answer

C

**Question. One function is selected from all the functions F: S, → where S = {1,2, 3, 4, 5,6} .The probability that it is onto function, is**

(a) 5/ 324

(b) 7/ 324

(c) 5/162

(d) 5/81

## Answer

A

**Question. A draws two cards at random from a pack of 52cards.****After returning them to the pack and shuffling it, B draws two cards at random. The probability that thier draws contain exactly one comman card is**

(a) 25/546

(b) 50/663

(c) 25/663

(d) None of these

## Answer

B

**Question. A and B stand in ring along with 10 other persons. If the arrangement is at random, the probability that there are exactly 3 person between A and B, is**

(a) 1 /11

(b) 2/11

(c) 3 /11

(d) 1/12

## Answer

B

**Question. A man throws a fair coin a number of times and gets 2 points for each head he throws and 1 point for each tail he throws. The probability that he gets exactly 6 points is**

(a) 21/32

(b) 23 /32

(c) 41/ 64

(d) 43/ 64

## Answer

D

**Question. In a random experiment, if the success is thrice that of failure. If the experiment is repeated 5 times, the probability that at least 4 times favourable is**

(a) 1053/2048

(b) 1003/2048

(c) 1203/2048

(d) None of these

## Answer

A

**Question. If x _{1} ,x_{2,}…,x_{50} are fifty real numbers such that x_{r} <x_{r+1 } for r =1,2, 3,…, 49. Five numbers out of these are picked up at random. The probability that the five numbers have x_{20} as the middle numbers, is**

## Answer

B

**Question. One Indian and four American men and their wives are to be seated randomly around a circular table.****Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is**

(a) 1/2

(b) 1/3

(c) 2/5

(d) 1/5

## Answer

C

**Question. In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on the question only if he ticks the correct answer. The candidate decides to tick answers at random. If he is allowed up to three chances of answer the answer the question, then the probability that he will get marks on it is**

(a) 1/3

(b) 2/3

(c) 1/5

(d) 2/15

## Answer

C

**Question. Three letters are written to there different persons and addresses on the three envelopes are also written. Without looking at the addresses, the letters are kept in these envelopes. The probability****that all the letters are not placed into their right envelopes is**

(a) 1/2

(b) 1/3

(c) 1/6

(d) 5/6

## Answer

B

**Question. Three natural numbers are taken at random from**

## Answer

C

**Question. **

(a) P (A ∩ B) =1/3

(b) A, B are exhaustive

(c) A, B are mutually exclusive

(d) A, B are independent

## Answer

A

**Question. apples are distributed at random among 6 persons. The probability that at least one of them will receive none is**

(a) 6/143

(b)^{14}C_{4}/^{15}C_{5}

(c) 137/143

(d) 135/143

## Answer

C

**Question. 7 white balls and 3 black balls are placed in a row at random. The probability that no two black balls are adjacent is**

(a) 1/2

(b) 7/15

(c) 2/15

(d) 1/3

## Answer

B

**Question. The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, a student has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two subjects. Which of the following relations are true?**

(a) p + m+ c +=19/20

(b) p+ m+c =27/20

(c) pmc =1/10

(d) pmc =1/4

## Answer

(B,C)

**Question. If E and F are two events with P(E) ≤ P(F) <0, then**

(a) occurrence of E ⇒ occurrence of F

(b) occurrence of F ⇒ occurrence of E

(c) non-occurrence of E ⇒ non-occurrence of F

(d) None of the above implications hold

## Answer

D

**Question. A card is selected at random from cards numbered as 00, 01, 02,…,99. An event is said to have occured. If product of digits of the card number is 16. If card is selected 5 times with replacement each time, then the probability that the event occurs exactly three times is**

## Answer

(B,D)

**Question.** **A second-order determinant is written down at random using the numbers 1, –1 as elements. The probability that the value of the determinant is non-zero is**

(a) 1/2

(b) 3/8

(c) 5/8

(d) 1/3

## Answer

A

**Question. A coin is tossed repeatedly. A and B call alternately for winning a prize of R.s.30. One who calls correctly first wins the prize. A starts the cell. Then, the expectation of**

(a) A is R.s.10

(b) B is R.s.10

(c) A is R.s.20

(d) B is R.s.20

## Answer

(B,C)

**Question.** Suppose a random variable X follows the Binomial distribution with parameters n and p, where 0< p< 1. If P (x = r) / P (x = n – r) is independent of n and r, then p equals to

(a) 1/2

(b) 1/3

(c) 1/5

(d) 1/7

**Answer**

A

**Question.** If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement atmost one is defective?

**Answer**

D

**Question.** The probability distribution of a discrete random variable X is given below

(a) 8

(b) 16

(c) 32

(d) 48

**Answer**

C

**Question.** If the probability that a person is not a swimmer is 0.3, then the probability that out of 5 persons 4 are swimmers is

(a) ^{5}C_{4}(0,7)^{4}(0,3)

(b) ^{5}C_{1}(0,7)(0,3)^{4}

(c) ^{5}C_{4}(0,7)(0,3)^{4}

(d) (0,7)^{4}(0,3)

**Answer**

A

**Question.** A and B are two students. Their chances of solving a problem correctly are 1/3 and 1/4, respectively. If the probability of their making a common error is, 1/20 and they obtain the same answer, then the probability of their answer to be correct is

(a) 1/12

(b) 1/40

(c) 13/120

(d) 10/13

**Answer**

D

**Question.** For the following probability distribution.

(a) 3

(b) 5

(c) 7

(d) 10

**Answer**

D

**Question.** Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has atleast one girl is

(a) 1/2

(b) 1/3

(c) 2/3

(d) 4/7

**Answer**

D

**Question.** Which one is not a requirement of a Binomial distribution?

(a) There are 2 outcomes for each trial

(b) There is a fixed number of trials

(c) The outcomes must be dependent on each other

(d) The probability of success must be the same for all the trials

**Answer**

C

**Question.** Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is

(a) 1/18

(b) 5/18

(c) 1/5

(d) 2/5

**Answer**

C

** Question. If eight coins are tossed together, then the probability of getting exactly 3 heads is**(a) 1/256

(b) 7/32

(c) 5/32

(d) 3/32

**Answer**

B

** Question. If P (A ∩ B) = 7/10 and P (B) = 17/20, then P(A/B) equals to**(a) 14/17

(b) 17/20

(c) 7/8

(d) 1/8

**Answer**

A

** Question. If P (A) = 0.4, P (B) = 0.8 and P (B / A) = 0.6, then P (A U B ) is equal to**(a) 0.24

(b) 0.3

(c) 0.48

(d) 0.96

**Answer**

D

**Question.** A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then probability that both are dead is

(a) 33/56

(b) 9/64

(c) 1/14

(d) 3/28

**Answer**

D

**Question.****A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, them the probability of getting exactly one red ball is**

(a) 45/196

(b) 135/392

(c) 15/56

(d) 15/29

**Answer**

C

**Question.** If A and B are two independent events with P (A) = 3/5 and P (B) = 4/9, then P (A’ ∩ B’) equals to

(a) 4/15

(b) 8/45

(c) 1/3

(d) 2/9

**Answer**

D

** Question. If A and B are such events that P (A) > 0 and P (B) ≠ 1, then P (A’ / B’) equals to**(a)1- P (A / B)

(b)1- P (A’ / B)

(c) 1- P (A U B)/P (B’)

(d) P (A’) /P (B’)

**Answer**

C

** Question. Two events E and F are independent. If P (E) = 0.3 and P (E u F ) = 0.5, then P (E /F ) – P (F /E) equals to**(a) 2/7

(b) 3/35

(c) 1/70

(d) 1/7

**Answer**

C

**Question.** A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is

(a) 3/28

(b) 2/21

(c) 1/28

(d) 167/168

**Answer**

A

**Question.** Three persons A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2, respectively. The probability of two hits is

(a) 0.024

(b) 0.188

(c) 0.336

(d) 0.452

**Answer**

B

**Question.**

(a) 1/5

(b) 4/5

(c) 1/2

(d) 1

**Answer**

D

** Question. In question 64 (above), P (B/A’) is equal to**(a) 1/5

(b) 3/10

(c) 1/2

(d) 3/5

**Answer**

D

**Question.** If A and B be two events such that P (A) = 3/8, P (B) = 5/8 and P (A U B) = 3/4, then P (A/B) ·**P (A’/B) is equal to**

(a) 2/5

(b) 3/8

(c) 3/20

(d) 6/25

**Answer**

D

**Question.** For the following probability distribution.

(a) 0

(b) -1

(c) -2

(d) -1.8

**Answer**

D

** Question. The probability of guessing correctly atleast 8 out of 10 answers on a true false type examination is**(a) 764

(b) 7/128

(c) 45/1024

(d) 7/41

**Answer**

B

**Question.** If two cards are drawn from a well shuffled deck of 52 playing cards with replacement, then the probability that both cards are queens, is

**Answer**

A

**Question.** If a die is thrown and a card is selected at random from a deck of 52playing cards, then the probability of getting an even number on the die and a spade card is

(a) 1/2

(b) 1/4

(c) 1/8

(d) 3/4

**Answer**

C

** Question. If two events are independent, then**(a) they must be mutually exclusive

(b) the sum of their probabilities must be equal to 1

(c) Both (a) and (b) are correct

(d) None of the above is correct

**Answer**

D

**Question.**

(a) 6/13

(b) 4/13

(c) 4/9

(d) 5/9

**Answer**

D

**Question.** If A and B are two events such that P

(a) 3/10

(b) 1/5

(c) 1/2

(d) 3/5

**Answer**

C

**Question.** If A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∩ B) = 0.5, then P (B’ U A) equals to

(a) 2/3

(b) 1/2

(c) 3/10

(d) 1/5

**Answer**

D

**Question.** Refer to question 74 above. If the probability that exactly two of the three balls were red, then the first ball being red, is

(a) 1/3

(b) 4/7

(c) 15/28

(d) 5/28

**Answer**

B

** Question. If the events A and B are independent, then P (A ∩ B) 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.** If A and B are two events and A ≠ ϕ, B ≠ ϕ, then

**Answer**

B

**Question.**

(a) 5/6

(b) 5/7

(c) 25/42

(d) 1

**Answer**

C

**Question.**

(a) 1/4

(b) 1/3

(c) 5/12

(d) 7/12

**Answer**

D

**Question.** If A and B are two events such that

(a) 1/12

(b) 3/4

(c) 1/4

(d) 3/16

**Answer**

C

** Question. If P (A)= 4/5 and P (A ∩ B) = 7/10, then P (B/A) is equal to**(a) 1/10

(b) 1/8

(c) 7/8

(d) 17/20

**Answer**

C

**True/False**

**Question.** If A and B are mutually exclusive events, then they will be independent also.

**Answer**

False

**Question.** Two independent events are always mutually exclusive.

**Answer**

False

**Question.** If A and B are two independent events, then P (A and B) = P (A) · P (B).

**Answer**

True

**Question.** Another name for the mean of a probability distribution is expected value.

**Answer**

True

**Question.** If P (A) > 0 and P (B) > 0. Then, A and B can be both mutually exclusive and independent.

**Answer**

False

**Question.** If A and B are two events such that P (A) > 0 and P (A) + P (B) > 1, then

**Answer**

False

**Question.** If A and B’ are independent events, then P(A’ U B) = 1 – P (A) P (B’).

**Answer**

True

**Question.** If A, B and C are three independent events such that

P (A) = P (B) = P (C) = p,

then P (atleast two of A, B and C occur) = 3**p ^{2}** – 2p

^{3}.

**Answer**

True

**Question.** If A and B are independent events, then A’ and B’ are also independent.

**Answer**

**Question.** If A and B are independent, then P (exactly one of A, B occurs)

= P (A) P (B’) + P (B) P (A’).

**Answer**

True