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

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Multiple Choice

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

Explanation:
The concept is how to combine conditional probability with the probability of the conditioning event to get the probability of both events happening. The probability of A and B together is P(A ∩ B) = P(B|A) × P(A). Plugging in the numbers gives 0.5 × 0.6 = 0.3. So the intersection probability is 0.3. The value 0.6 would be P(A) alone, not the overlap with B; 0.5 is P(B|A) itself, not the overlap; and 0.9 isn’t derived from these values.

The concept is how to combine conditional probability with the probability of the conditioning event to get the probability of both events happening. The probability of A and B together is P(A ∩ B) = P(B|A) × P(A). Plugging in the numbers gives 0.5 × 0.6 = 0.3. So the intersection probability is 0.3. The value 0.6 would be P(A) alone, not the overlap with B; 0.5 is P(B|A) itself, not the overlap; and 0.9 isn’t derived from these values.

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