If $P(A) = \frac{7}{{13}}$, $P(B) = \frac{9}{{13}}$ and $P(A \cap B) = \frac{4}{{13}}$, then $P\left( {{A^\prime }/B} \right)$ is equal to

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

$\therefore$ $P\left( {{A^\prime }/B} \right) = \frac{{P\left( {{A^\prime } \cap B} \right)}}{{P(B)}} = \frac{{P(B) - P(A \cap B)}}{{P(B)}}$

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