If P(A) = 0.5 and P(B) = 0.6 and A and B are independent, P(A ∩ B) equals?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If P(A) = 0.5 and P(B) = 0.6 and A and B are independent, P(A ∩ B) equals?

Explanation:
Independence means the chance both events occur is the product of their individual probabilities: P(A ∩ B) = P(A) × P(B). With P(A) = 0.5 and P(B) = 0.6, multiply to get 0.5 × 0.6 = 0.30. So the probability of both happening is 0.30. This value stays within the bounds set by the marginals, since the intersection cannot exceed either P(A) or P(B). The other options are not possible because they would violate independence or exceed the available probabilities. Hence the correct result is 0.30.

Independence means the chance both events occur is the product of their individual probabilities: P(A ∩ B) = P(A) × P(B). With P(A) = 0.5 and P(B) = 0.6, multiply to get 0.5 × 0.6 = 0.30. So the probability of both happening is 0.30. This value stays within the bounds set by the marginals, since the intersection cannot exceed either P(A) or P(B). The other options are not possible because they would violate independence or exceed the available probabilities. Hence the correct result is 0.30.

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