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