If $2P(A) = P(B) =\frac{5}{13}$ and $P(A|B) =\frac{2}{5}$, then $P(A∩B)$ is

$\frac{2}{13}$

The correct answer is Option (2) → $\frac{2}{13}$

Given:

$2P(A) = P(B) = \frac{5}{13}$

$P(A \mid B) = \frac{2}{5}$

Step 1: Find $P(A)$ and $P(B)$

$2P(A) = \frac{5}{13} \Rightarrow P(A) = \frac{5}{26}$
$P(B) = \frac{5}{13}$

Step 2: Use conditional probability:

$P(A \mid B) = \frac{P(A \cap B)}{P(B)} \Rightarrow \frac{2}{5} = \frac{P(A \cap B)}{5/13}$

$\Rightarrow P(A \cap B) = \frac{2}{5} \cdot \frac{5}{13} = \frac{2}{13}$