Question
Class 11MathematicsProbability

If A and B are any two events having P(A ∪ B) = 1/2 and P(Ā) = 2/3, then the probability of Ā ∩ B is?

Verified Answer

P(A ∪ B) = 1/2

⇒ P(A ∪ (B − A)) = 1/2

⇒ P(A) + P(B − A) = 1/2 (since A and B − A are mutually exclusive)

⇒ 1 − P(Ā) + P(B − A) = 1/2

⇒ 1 − 2/3 + P(B − A) = 1/2

⇒ P(B − A) = 1/6

∴ P(Ā ∩ B) = 1/6 (since Ā ∩ B = B − A)