If P(A) = 0.6 and P(B) = 0.5 and A and B are independent, what is P(A and B)?

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Multiple Choice

If P(A) = 0.6 and P(B) = 0.5 and A and B are independent, what is P(A and B)?

Explanation:
The main idea is that when two events are independent, the probability that both occur is the product of their probabilities: P(A ∩ B) = P(A) × P(B). Here that’s 0.6 × 0.5 = 0.30. So the chance of both A and B happening is 0.30. The other numbers don’t reflect the intersection under independence: 0.60 would be just P(A) if B had no impact, and 0.50 would be just P(B). The product 0.30 is the correct joint probability when the events don’t influence each other.

The main idea is that when two events are independent, the probability that both occur is the product of their probabilities: P(A ∩ B) = P(A) × P(B). Here that’s 0.6 × 0.5 = 0.30. So the chance of both A and B happening is 0.30.

The other numbers don’t reflect the intersection under independence: 0.60 would be just P(A) if B had no impact, and 0.50 would be just P(B). The product 0.30 is the correct joint probability when the events don’t influence each other.

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