# MCQ Questions for Class 12 Maths Chapter 13 Probability 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

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

## Answer

Answer: (a) 4 : 3

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

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

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

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

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

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

## Answer

Answer: (c) A ⊂ B

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Answer

Answer: (a) 0.3

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

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

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

## Answer

Answer: (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

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

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

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

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

## Answer

Answer: (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

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

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

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

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

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

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

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

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

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

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)

## Answer

Answer: (c) P(a). P(b)

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