If $P(A)=\frac{3}{10}, P(B)=\frac{2}{5}$ and $P(A ∪ B)=\frac{3}{5}, $ then $P(B|A)+P(A|B)$ is equal to :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{7}{12}$
$P(A)=\frac{3}{10}, P(B)=\frac{2}{5}$ and $P(A ∪ B)=\frac{3}{5}$
$P(A∩B)=-P(A ∪ B)+P(A)+P(B)=\frac{1}{10}$
so $P(B|A)+P(A|B)=P(A∩B)(\frac{1}{P(A)}+\frac{1}{P(B)})=\frac{7}{12}$