Two statements are given, one labelled ...

CBSE Class 12 Math 2026 All Sets Solved Paper

Question : 19 of 20

Marks: +1, -0

Two statements are given, one labelled Assertion (A) and other labelled Reason (R).

Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is

\;\frac{2}{3}

Reason (R) : For any two events A and

B,\; P(A \mid B)=\frac{P(A \cup B)}{P(B)}

Select the correct answer from the options (A), (B), (C) and (D) as given below.

Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.

Solution:

Here, we define event

A = Getting a prime number on die.

B = Getting an odd number on die.

Given that number appearing on the die is odd, so we need to calculate probability that number is prime too.

Prime number on die = 2, 3, 5

P(A)=\frac{3}{6}=\frac{1}{2}

Odd number on die

=1,3,5

P(B)=\frac{3}{6}=\frac{1}{2}

A \cap B=\{3,5\}

P(A \cap B)=\frac{2}{6}=\frac{1}{3}

P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{1}{3}\frac{1}{2}=\frac{2}{3}.

So assertion is true.

In reason, given that

P(A \mid B)=\frac{P(A \cup B)}{P(B)}

, which is wrong statement, as

P(A \mid B)=\frac{P(A \cap B)}{P(B)}

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