If $2P(A)=P(B)=\frac{5}{13}$ and $P(\frac{A}{B})=\frac{2}{5},$ then the value of $P(A∪B)$ is :

$\frac{11}{26}$

The correct answer is Option (3) → $\frac{11}{26}$

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

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

so $P(A∪B)=P(A)+P(B)-P(A∩B)$

$=\frac{5}{26}+\frac{10}{26}-\frac{4}{26}=\frac{11}{26}$