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Given that P(A)=2/5, P(B)=3/10, and P(A ∩ B̄)=1/5, find the value of P(A'|B') × P(B'|A').
- 5/6
- 5/7
- 25/42
- 1
Correct answer: 25/42
Solution
P(A∩B)=P(A)-P(A∩B')=2/5-1/5=1/5, P(AuB)=2/5+3/10-1/5=1/2, so P(A'∩B')=1/2. Then P(A'|B')=(1/2)/(7/10)=5/7 and P(B'|A')=(1/2)/(3/5)=5/6; product = 25/42.
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