It is given that the events A and B are such that $P(A) =\frac{1}{4}, P(A/B)=\frac{1}{2}$ and $P(B/A)=\frac{2}{3}$. Then, P (B) is

$\frac{2}{3}$ $\frac{1}{2}$ $\frac{1}{6}$ $\frac{1}{3}$

$\frac{1}{3}$

We have, $P(A ∩ B) = P(A) P(B/A)$ $∴ P(A ∩ B) =\frac{1}{4}× \frac{2}{3}=\frac{1}{6}$ Now, $P(A/B)=\frac{P(A ∩ B)}{P(B)}⇒ \frac{1}{2}=\frac{1}{6}×\frac{1}{P(B)}⇒P(B)=\frac{1}{3}$