If $P(A)=\frac{2}{5}, P(B)=\frac{3}{10}$ and $P(A∩B)=\frac{1}{5}, $ then $P(A|B).(P(B'/A')$ is equal to :

$\frac{5}{9}$

The correct answer is Option (3) → $\frac{5}{9}$

$P(A|B).P(\overline B|\overline A)=\frac{P(A∩B)(1-P(A∪B))}{P(B)P(\overline A)}$

$[∵ P(\overline B|\overline A)=P(\overline{A∪B})=1-P(A∪B)]\\ [P(A∪B)=P(A)+P(B)-P(A∩B)]$

$=\frac{5}{9}$