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Let A and B be events with P(A)=1/2 and P(B)=2/3. Which statement below is false?
- P(A ∪ B) is at least 2/3
- P(A ∩ B') is at least 1/3
- P(A ∩ B) lies between 1/6 and 1/2
- P(A' ∩ B) lies between 1/6 and 1/2
Correct answer: P(A ∩ B') is at least 1/3
Solution
The statement P(A ∩ B') is at least 1/3 is false because it suggests that the probability of event A occurring while event B does not occur is greater than or equal to 1/3, which is not supported by the given probabilities of A and B.
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