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If the probabilities of two events A and B are equal, with P(A)=P(B)=x, and P(A ∩ B)=P(A' ∩ B')=1/3, what is the value of x?
- 1/2
- 1/3
- 1/4
- 1/6
Correct answer: 1/2
Solution
P(A'/\B') = 1 - P(AUB) = 1/3, so P(AUB) = 2/3. Then P(AUB) = P(A)+P(B)-P(A/\B) = 2x - 1/3 = 2/3, giving 2x = 1, x = 1/2.
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