Let A and B be two events such that $P(A) = 0.2, P(B) = 0.4, P(B|A) = 0.5$

Choose the correct answer from the options given below:

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

The correct answer is Option (1) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

Given:

$P(A) = 0.2$,   $P(B) = 0.4$,   $P(B|A) = 0.5$

(A) $P(A \cap B) = P(A) \cdot P(B|A) = 0.2 \cdot 0.5 = 0.1$ ⇒ Match with (IV)

(B) $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.1}{0.4} = 0.25$ ⇒ Match with (III)

(C) $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.2 + 0.4 - 0.1 = 0.5$ ⇒ Match with (I)

(D) $P(A') = 1 - P(A) = 1 - 0.2 = 0.8$ ⇒ Match with (II)