If \(A\) and \(B\) are two events such that \(P(A) = \displaystyle\frac{1}{2}, P(B) = \frac{1}{3}, P(B|A) = \frac{1}{4}\), then \(P(A|B)\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{3}{8}\)
By the definition of conditional probability, \(P(A \cap B) = P(A)\,P(B|A)\):
\( \displaystyle P(A \cap B) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \)
\( \displaystyle P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{1/8}{1/3} = \frac{3}{8} \)