If \(2P(A) = P(B) = \displaystyle\frac{5}{13}\) and \(P(A|B) = \displaystyle\frac{2}{5}\), then \(P(A \cap B)\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{2}{13}\)
By the definition of conditional probability, \(P(A|B) = \frac{P(A \cap B)}{P(B)}\), so
\(\displaystyle P(A \cap B) = P(A|B)\,P(B) = \frac{2}{5} \times \frac{5}{13} = \frac{2}{13}\)
The value \(P(A) = \frac{5}{26}\) is not needed.