**Answer : (d) \(\frac{1}{3}\)**

**Given, **

P(B/A)** =\(\frac{P(A\,\cap\,B)}{P(A)}\)**

**\(P(A\,\cap\,B)= P(B/A)\times P(A)=\frac{2}{3}\times \frac{1}{4} = \frac{1}{6}\)**

Now P(A/B) = \(\frac{P(A\,\cap\,B)}{P(B)}\)

= **\(\frac{1}{2} = \frac{1}{6}\times \frac{1}{P(B)} \implies P(B)=\frac{2}{6}= \frac{1}{3}\)**