If $P(A) =\frac{3}{10}, P(B) =\frac{2}{5}$ and $P(A∪B) =\frac{3}{5}$ then the value of $P(B|A) + P(A|B)$ is:

$\frac{7}{12}$

The correct answer is Option (4) → $\frac{7}{12}$

Given:

$P(A)=\frac{3}{10},\quad P(B)=\frac{2}{5}=\frac{4}{10},\quad P(A\cup B)=\frac{3}{5}=\frac{6}{10}$

Using $P(A\cup B)=P(A)+P(B)-P(A\cap B)$:

$\frac{6}{10}=\frac{3}{10}+\frac{4}{10}-P(A\cap B)$

$\Rightarrow P(A\cap B)=\frac{1}{10}$

$P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{\frac{1}{10}}{\frac{3}{10}}=\frac{1}{3}$

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{1}{10}}{\frac{4}{10}}=\frac{1}{4}$

$P(B|A)+P(A|B)=\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$