Question

Assertion (A) : If $P (A/B) = P (B/A ). A, B$ are two non. M.E. events then $P(A ) = P(B)$.
Reason (R) : For non mutually exclusive events $A \cap B \ne \phi$ and $P(A/B) = \frac{P(A \cap B)}{P(B)}$,
$P(B /A) = \frac{P(A \cap B)}{P(A)}$.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

$P(A/B) = P(B/A)$
$\Rightarrow \frac{P(A \cap B)}{P(B)} = \frac{P(B\cap A)}{P(A)}$
$\Rightarrow P(A) = P(B)$
$\Rightarrow $ Assertion (A) follows by Reason (R).