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Let A and B be two events with P(Ā)=0.3, P(B)=0.4, and P(A ∩ B̄)=0.5. Find P(B | A ∪ B̄).

1. 0.9
2. 0.5
3. 0.6
4. 0.25

Correct answer: 0.25

Solution

P(A)=0.7; P(A∩B̄)=0.5 gives P(A∩B)=0.2. B∩(A∪B̄)=A∩B=0.2. P(A∪B̄)=0.7+0.6-0.5=0.8. So P(B|A∪B̄)=0.2/0.8=0.25.

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