Let $P(A) = \frac{7}{13}$, $P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$. Then $P(A' \mid B)$ is equal to

$\frac{5}{9}$

The correct answer is Option (4) → $\frac{5}{9}$ ##

Here, $P(A) = \frac{7}{13}, P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$

$∴P(A' \mid B) = \frac{P(A' \cap B)}{P(B)} = \frac{P(B) - P(A \cap B)}{P(B)}$

$= \frac{\frac{9}{13} - \frac{4}{13}}{\frac{9}{13}} = \frac{5/13}{9/13} = \frac{5}{9}$