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A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P (B′ ∩ A) equals A. 2/3 B. 1/2 C. 3/10 D. 1/5 Select the correct answer from above options

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We have, P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5 Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) [Additive Law of Probability] ⇒ 0.5 = 0.4 + 0.3 – P(A ∩ B) ⇒ P(A ∩ B) = 0.7 – 0.5 ⇒ P(A ∩ B) = 0.2 ∴ P(B’ ∩ A) = P(B’) P(A) = [1 – P(B)]× P(A) [sum of the probabilities of an event and its complement is 1] = P(A) – P(A)P(B) = P(A) – P(A ∩ B) = 0.4 – 0.2 = 0.2 = 1/5 Hence, the correct option is D

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