If A and B are two independent events with \(P(A) = \displaystyle\frac{1}{5}\) and \(P(B) = \displaystyle\frac{1}{3}\), then \(P(A'/B)\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{4}{5}\)
Since A and B are independent, A′ and B are also independent, so knowing that B has happened does not change the probability of A′:
\( \displaystyle P(A'/B) = \frac{P(A' \cap B)}{P(B)} = \frac{P(A')\,P(B)}{P(B)} = P(A') \)
\( \displaystyle P(A') = 1 - \frac{1}{5} = \frac{4}{5} \)