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

Question

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 (a) \(\frac{1}{2}\) (b) \(\frac{2}{3}\) (c) \(\frac{1}{6}\) (d) \(\frac{1}{3}\) Select the correct answer from above options

Answer 1

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