Check the below NCERT MCQ Questions for Class 12 Maths Chapter 13 Probability with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Probability Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Probability Class 12 MCQs Questions with Answers

Question 1.
If A and B are two independent events, then
(a) P(A∩B) = P(a) × P(b)
(b) P(AB) = 1 – P(A’) P(B’)
(c) P(AB) = 1 + P (A’) P(B’) P(A’)
(d) P (AB) = $$\frac{P(A’)}{P(B’)}$$

Answer: (a) P(A∩B) = P(a) × P(b)

Question 2.
The probability of an event is $$\frac{3}{7}$$. Then odd against the event is
(a) 4 : 3
(b) 7 : 3
(c) 3 : 7
(d) 3 : 4

Question 3.
A pair of dice are rolled. The probability of obtaining an even prime number on each die is
(a) $$\frac{1}{36}$$
(b) $$\frac{1}{12}$$
(c) $$\frac{1}{6}$$
(d) 0

Answer: (a) $$\frac{1}{36}$$

Question 4
If P(a) = $$\frac{3}{8}$$, P(b) = $$\frac{1}{3}$$ and P(A∩B) = — then P (A’ ∩B’)
(a) $$\frac{13}{24}$$
(b) $$\frac{13}{8}$$
(c) $$\frac{13}{9}$$
(d) $$\frac{13}{4}$$

Answer: (a) $$\frac{13}{24}$$

Question 5.
P(A∩B) = $$\frac{3}{8}$$, P(b) = $$\frac{1}{2}$$ and P(a) = $$\frac{1}{4}$$ then P($$\frac{B’}{A’}$$) =
(a) $$\frac{3}{5}$$
(b) $$\frac{5}{8}$$
(c) $$\frac{3}{8}$$
(d) $$\frac{5}{6}$$

Answer: (d) $$\frac{5}{6}$$

Question 6.
If A and B are two events such that P(a) ≠ 0 and P($$\frac{B}{A}$$) = 1 then
(a) P($$\frac{A}{B}$$) = 1
(b) P($$\frac{B}{A}$$) = 1
(c) P($$\frac{A}{B}$$) = 0
(d) P($$\frac{B}{A}$$) = 0

Answer: (b) P($$\frac{B}{A}$$) = 1

Question 7.
If P (a) = $$\frac{3}{8}$$, P(b) = $$\frac{1}{2}$$ and P(A∩B) = $$\frac{1}{4}$$ then P($$\frac{A’}{B’}$$) =
(a) $$\frac{1}{4}$$
(b) $$\frac{1}{3}$$
(c) $$\frac{3}{4}$$
(d) $$\frac{3}{8}$$

Answer: (b) $$\frac{1}{3}$$

Question 8.
If A and B are two events such that P(a) ≠ 0 and P($$\frac{B}{A}$$) = 1, then
(a) B ⊂ A
(b) B = φ
(c) A ⊂ B
(d) A ∩ B = φ

Question 9.
If A and B are any two events such that P(a) + P(b) – P(A∩B) = P(a) then
(a) P($$\frac{B}{A}$$) = 1
(b) P($$\frac{B}{A}$$) = 0
(c) P($$\frac{A}{B}$$) = 1
(d) P($$\frac{A}{B}$$) = 0

Answer: (c) P($$\frac{A}{B}$$) = 1

Question 10.
If A and B are events such that P (A∪B) = $$\frac{3}{4}$$. P(A∩B) = $$\frac{1}{4}$$, P(a) = $$\frac{2}{3}$$ then P(AB) is
(a) $$\frac{3}{8}$$
(b) $$\frac{5}{8}$$
(c) $$\frac{5}{12}$$
(d) $$\frac{1}{4}$$

Answer: (b) $$\frac{5}{8}$$

Question 11.
If one card is drawn out of 52 playing cards, the probability that it is an dice is
(a) $$\frac{1}{26}$$
(b) $$\frac{1}{13}$$
(c) $$\frac{1}{52}$$
(d) $$\frac{1}{4}$$

Answer: (b) $$\frac{1}{13}$$

Question 12.
The chance of getting a doublet with 2 dice is
(a) $$\frac{2}{3}$$
(b) $$\frac{1}{6}$$
(c) $$\frac{5}{6}$$
(d) $$\frac{5}{36}$$

Answer: (b) $$\frac{1}{6}$$

Question 13.
Two number are chosen, one by one without replacement from the set of number A = {1, 2, 3, 4, 5, 6} then the probability that minimum value of two number chosen is less than 4 is
(a) $$\frac{14}{15}$$
(b) $$\frac{1}{15}$$
(c) $$\frac{1}{5}$$
(d) $$\frac{8}{5}$$

Answer: (b) $$\frac{1}{15}$$

Question 14.
If P(x) = $$\frac{2}{15}$$; y = 1, 2, 3, 4, 5, 0 otherwise then P|x = 1 or 2| is
(a) $$\frac{1}{15}$$
(b) $$\frac{2}{15}$$
(c) $$\frac{1}{5}$$
(d) None of these

Answer: (c) $$\frac{1}{5}$$

Question 15.
Five horse are in a race. Mr. A select two of the horses at random and best on them. The probability that Mr. A select the winning horses is
(a) $$\frac{4}{5}$$
(b) $$\frac{3}{5}$$
(c) $$\frac{1}{5}$$
(d) $$\frac{2}{5}$$

Answer: (d) $$\frac{2}{5}$$

Question 16.
The probability of India w inning a test match against. West Indies is $$\frac{1}{2}$$. Assuming independence from match to match the probability that in a match series India second win occurs at the third test is
(a) $$\frac{1}{6}$$
(b) $$\frac{1}{4}$$
(c) $$\frac{1}{2}$$
(d) $$\frac{2}{3}$$

Answer: (b) $$\frac{1}{4}$$

Question 17.
Three distinct numbers.are selected from First 100 natural numbers. The probability divisible by 2 and 3 is
(a) $$\frac{9}{25}$$
(b) $$\frac{4}{35}$$
(c) $$\frac{4}{55}$$
(d) $$\frac{4}{1155}$$

Answer: (d) $$\frac{4}{1155}$$

Question 18.
The probability that A speaks truth is $$\frac{4}{5}$$ while this probability for B is $$\frac{3}{4}$$. The probability that they contradict each others when asked to speak ana fact is
(a) $$\frac{7}{20}$$
(b) $$\frac{1}{5}$$
(c) $$\frac{3}{20}$$
(d) $$\frac{4}{5}$$

Answer: (d) $$\frac{4}{5}$$

Question 19.
Two dice are tossed once. The probability of getting an even number at the first dice ora total of 8 is
(a) $$\frac{1}{36}$$
(b) $$\frac{3}{36}$$
(c) $$\frac{11}{36}$$
(d) $$\frac{5}{9}$$

Answer: (d) $$\frac{5}{9}$$

Question 20.
The mean and the variance of binomial distribution are 4 and 2, respectively. Then the probability of 2 success
(a) $$\frac{128}{256}$$
(b) $$\frac{219}{256}$$
(c) $$\frac{7}{64}$$
(d) $$\frac{28}{256}$$

Answer: (c) $$\frac{7}{64}$$

Question 21.
A pair of dice are rolled. The probability of obtaining an even prime number on each dice is
(a) $$\frac{1}{36}$$
(b) $$\frac{1}{12}$$
(c) $$\frac{1}{6}$$
(d) 0

Answer: (a) $$\frac{1}{36}$$

Question 22.
If A, B are two events associated with same random experiment such that P(a) = 0.4, P(b) = 0.8 and P(B/A) = 0.6 then P(A/B) is
(a) 0.3
(b) 0.4
(c) 0.5
(d) 0.6

Question 23.
If P(a) = $$\frac{3}{8}$$, P(b) = $$\frac{5}{8}$$, P(A∪B) = $$\frac{3}{4}$$ then p($$\frac{B}{A}$$) is
(a) $$\frac{3}{47}$$
(b) $$\frac{5}{49}$$
(c) $$\frac{2}{3}$$
(d) $$\frac{1}{4}$$

Answer: (c) $$\frac{2}{3}$$

Question 24.
An urn contain’s balls of which 3 are red, 4 are blue and 2 are green, 3 balls are drawn at random without replacement from the urn. The probability that the 3 balls haye different colours is
(a) $$\frac{1}{3}$$
(b) $$\frac{2}{7}$$
(c) $$\frac{1}{21}$$
(d) $$\frac{2}{23}$$

Answer: (b) $$\frac{2}{7}$$

Question 25.
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. A consists 4 outcomes, the number of outcomes that B must have so that A and B are independent is
(a) 2, 4 or 8
(b) 36 or 9
(c) 4 or 8
(d) 5 or 10

Question 28.
If P(a) = $$\frac{4}{5}$$ and P(A∩B) = $$\frac{7}{10}$$, then P(B/A) is equal
(a) $$\frac{1}{10}$$
(b) $$\frac{1}{8}$$
(c) $$\frac{7}{8}$$
(d) $$\frac{17}{20}$$

Answer: (d) $$\frac{17}{20}$$

Question 29.
If P(A∩B) = $$\frac{7}{10}$$ and P(b) = $$\frac{17}{20}$$, then P(A|B) equals
(a) $$\frac{14}{17}$$
(b) $$\frac{17}{20}$$
(c) $$\frac{7}{8}$$
(d) $$\frac{1}{8}$$

Answer: (a) $$\frac{14}{17}$$

Question 30.
If P(a) = $$\frac{7}{10}$$ P(b) = $$\frac{7}{10}$$ and P(A∪B) = $$\frac{7}{10}$$ then P (B|A) + P(A|B) equals
(a) $$\frac{1}{4}$$
(b) $$\frac{1}{3}$$
(c) $$\frac{5}{12}$$
(d) $$\frac{7}{12}$$

Answer: (d) $$\frac{7}{12}$$

Question 31.
If P(a) = $$\frac{2}{5}$$, P(b) = $$\frac{3}{10}$$ and P (A∩B) = $$\frac{1}{5}$$, then P (A’|B’). P(B’|A’) is equal to
(a) $$\frac{5}{6}$$
(b) $$\frac{5}{7}$$
(c) $$\frac{25}{42}$$
(d) 1

Answer: (c) $$\frac{25}{42}$$

Question 32.
If P(a) = 0,4, P(b) = 0.8 and P(B|A) = 0.6 then P(A∪B) is equal to
(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96

Question 33.
If A and B are two events and A ≠ Φ, B ≠ Φ, then
(a) P (A|B) = P (a). P (b)
(b) P (A|B) = $$\frac{P(A∩B)}{P(B)}$$
(c) P (A + B). P (B|A) = 1
(d) P (A|B) = P (a) | P (b)

Answer: (b) P (A|B) = $$\frac{P(A∩B)}{P(B)}$$

Question 34.
A and B are events such that P(a) = 0.4, P(b) = 0.3 and P(A∪B) = 0.5. Then P(B∩A) equals
(a) $$\frac{2}{3}$$
(b) $$\frac{1}{2}$$
(c) $$\frac{3}{10}$$
(d) $$\frac{1}{5}$$

Answer: (d) $$\frac{1}{5}$$

Question 35.
You are given that A and B are two events such that P(b) = $$\frac{3}{5}$$, P(A|B) = $$\frac{1}{2}$$ and P (A∪B) = $$\frac{4}{5}$$, then P(a) equals
(a) $$\frac{3}{10}$$
(b) $$\frac{1}{5}$$
(c) $$\frac{1}{2}$$
(d) $$\frac{3}{5}$$

Answer: (c) $$\frac{1}{2}$$

Question 36.
You are given that A and B are two events such that P(b) = $$\frac{3}{5}$$, P(A|B) = $$\frac{1}{2}$$ and P (A∪B) = then P(B|A’) equals
(a) $$\frac{1}{5}$$
(b) $$\frac{3}{10}$$
(c) $$\frac{1}{2}$$
(d) $$\frac{3}{5}$$

Answer: (d) $$\frac{3}{5}$$

Question 37.
If P(b) = $$\frac{1}{5}$$, P(A|B) = $$\frac{1}{2}$$ and P(A∪B) = $$\frac{4}{5}$$ then P (A∪B)’ + P (A’∪B) =
(a) $$\frac{1}{5}$$
(b) $$\frac{4}{5}$$
(c) $$\frac{1}{2}$$
(d) $$\frac{3}{5}$$

Answer: (d) $$\frac{3}{5}$$

Question 38.
Let P (a) = $$\frac{7}{13}$$, P(b) = $$\frac{9}{13}$$ and P (A∪B) = $$\frac{9}{13}$$, Then P(A’|B) is equal to
(a) $$\frac{6}{13}$$
(b) $$\frac{4}{13}$$
(c) $$\frac{4}{9}$$
(d) $$\frac{5}{9}$$

Answer: (d) $$\frac{5}{9}$$

Question 39.
If A and B are such that events that P(a) > 0 and P(b) ≠ 1, then P (A’|B’) equal
(a) 1 – P (A|B)
(b) 1 – P(A’|B)
(c) $$\frac{1-P(A∪B)}{P(B’)}$$
(d) p(A’) | P(B’)

Answer: (c) $$\frac{1-P(A∪B)}{P(B’)}$$

Question 40.
If two events are independent, then
(a) they must be mutually exclusive
(b) the sum of their probabilities must be equal to 1
(c) (a) and (b) both are correct
(d) None of the above is correct

Answer: (d) None of the above is correct

Question 41.
If A and B are two independent events with P(a) = $$\frac{3}{5}$$ and P (b) = $$\frac{4}{9}$$, then P (A’∩B’) equals
(a) $$\frac{4}{15}$$
(b) $$\frac{8}{15}$$
(c) $$\frac{1}{3}$$
(d) $$\frac{2}{9}$$

Answer: (d) $$\frac{2}{9}$$

Question 42.
Let A and B two event such that P(a) = $$\frac{3}{8}$$, P(b) = $$\frac{5}{8}$$ and P(A∪B) = $$\frac{3}{4}$$. Then P(A|B).P(A’|B) is equal to
(a) $$\frac{2}{5}$$
(b) $$\frac{3}{8}$$
(c) $$\frac{3}{20}$$
(d) $$\frac{6}{25}$$
Ans. (d)

Answer: (d) $$\frac{6}{25}$$

Question 43.
If the event 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)