If A and B are independent and P(A) = 0.4, P(B) = 0.6, what is P(A ∩ B)?

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Multiple Choice

If A and B are independent and P(A) = 0.4, P(B) = 0.6, what is P(A ∩ B)?

Explanation:
When two events are independent, the chance that both happen is the product of their individual probabilities. So P(A ∩ B) = P(A) × P(B) = 0.4 × 0.6 = 0.24. This value passes a quick sanity check: it’s smaller than each of the individual probabilities, which makes sense because both events happening is more restrictive than either happening alone. If the events weren’t independent, you’d use P(A ∩ B) = P(A) × P(B | A), but independence means P(B | A) = P(B). The other numbers would correspond to either P(A) alone, P(B) alone, or a square probability that doesn’t apply here.

When two events are independent, the chance that both happen is the product of their individual probabilities. So P(A ∩ B) = P(A) × P(B) = 0.4 × 0.6 = 0.24. This value passes a quick sanity check: it’s smaller than each of the individual probabilities, which makes sense because both events happening is more restrictive than either happening alone. If the events weren’t independent, you’d use P(A ∩ B) = P(A) × P(B | A), but independence means P(B | A) = P(B). The other numbers would correspond to either P(A) alone, P(B) alone, or a square probability that doesn’t apply here.

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