**CBSE Class 12 Maths – MCQ and Online Tests – Unit 13 – Probability**

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

**CBSE Class 12 Maths – MCQ and Online Tests – Unit 13 – Probability**

Question 1.

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 2.

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 3.

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 4.

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 5.

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 6.

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 7.

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 8.

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 9.

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 10.

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 11.

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 12.

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 13.

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 14.

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 15.

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 16.

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 17.

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 18.

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 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.

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 21.

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 22.

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 23.

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 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 26.

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 27.

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 28.

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 29.

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 30.

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) \(\frac{6}{25}\)

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