Question

Assertion: Consider the two events A and B such that n(A) = n(B) and `P(A/B) = P(B/A)`.

Reason: The events A and B are mutually exclusive.

Options

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Assertion is false and Reasons true.

Answer 1

Assertion is true and Reason is false.

Explanation:

Given, n(A) = n(B)

`P(A/B) = (n(A ∩ B))/(n(B))`

And `P(B/A) = (n(A ∩ B))/(n(A))`   

= `(n(A ∩ B))/(n(B))`

`P(A/B) = P(B/A)`   ...[∵ n(A) = n(B)]

So, Assertion is true.

Mutually exclusive events have no intersection, making the conditional probability zero.

So, Reason is false.