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Let A and B be events with P(A ∪ B)=3/4, P(A ∩ B)=1/4, and P(Ā)=2/3. Find the value of P(Ā ∩ B).

1. 5/12
2. 3/8
3. 5/8
4. 1/4

Correct answer: 5/12

Solution

P(A)=1-2/3=1/3. From P(AuB)=P(A)+P(B)-P(A∩B): 3/4=1/3+P(B)-1/4, so P(B)=2/3. Then P(A'∩B)=P(B)-P(A∩B)=2/3-1/4=5/12.

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