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

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

• A. 0.40
• B. 0.16
• C. 0.24
• D. 0.60

Answer: (C)

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.