If $P(A) =\frac{1}{4}, P(\overline{B})=\frac{1}{2}$ and $ P(A ∪ B)=\frac{5}{9}$, then $ P(A /B)$ is
Answer & explanation
Correct answer: option 3
We have,
$ P(A ∪ B)=\frac{5}{9}$
$⇒ P(A) +P(B) -P(A ∩ B)=\frac{5}{9}$
$⇒ \frac{1}{4}+\frac{1}{2}-P(A ∩ B)=\frac{5}{9}$
$⇒ P(A ∩ B)=\frac{7}{36}$
$⇒ P(B) P(A/B)=\frac{7}{36}$
$⇒ \frac{1}{2}× P(A/B)=\frac{7}{36}⇒ P(A/B)=\frac{7}{18}$