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
Answer & explanation
Correct answer: option 4
We have,
$P(A ∩ B) = P(A) P(B/A)$
$∴ P(A ∩ B) =\frac{1}{4}× \frac{2}{3}=\frac{1}{6}$
Now, $P(A/B)=\frac{P(A ∩ B)}{P(B)}⇒ \frac{1}{2}=\frac{1}{6}×\frac{1}{P(B)}⇒P(B)=\frac{1}{3}$