If A and B are independent events such that \(P(A|B) =\displaystyle\frac{1}{3}\) and \(P(B) =\displaystyle\frac{1}{2}\) then the value of \(P(A \cap B)\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{6}\)
By the definition of conditional probability:
\( \displaystyle P(A \cap B) = P(A|B) \cdot P(B) \)
\( \displaystyle = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \)
(Since A and B are independent, \(P(A) = P(A|B) = \frac{1}{3}\), and \(P(A)P(B)\) gives the same \(\frac{1}{6}\).)