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

Question

Philoid · Accepted Answer

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

Hence, the correct option is D