If P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?

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Multiple Choice

If P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?

Explanation:
Joint probability is found by multiplying the probability of the conditioning event by the probability of the event of interest given that conditioning. So P(A ∩ B) = P(A|B) × P(B) = 0.5 × 0.6 = 0.30. The probability that both A and B occur is 0.30. The other values don’t come from the product of 0.5 and 0.6, so they don’t represent the intersection.

Joint probability is found by multiplying the probability of the conditioning event by the probability of the event of interest given that conditioning. So P(A ∩ B) = P(A|B) × P(B) = 0.5 × 0.6 = 0.30. The probability that both A and B occur is 0.30. The other values don’t come from the product of 0.5 and 0.6, so they don’t represent the intersection.

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