Which statement correctly distinguishes independence from mutual exclusivity between two events A and B?

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Multiple Choice

Which statement correctly distinguishes independence from mutual exclusivity between two events A and B?

Explanation:
Independence means the occurrence of one event does not affect the probability of the other, which is captured by the joint probability P(A ∩ B) = P(A) P(B). Mutual exclusivity means the two events cannot happen at the same time, so their intersection is impossible and P(A ∩ B) = 0. The statement that states both of these precisely names the two distinct relationships: independence uses the product rule, while mutual exclusivity requires a zero intersection. The other options mix up these ideas—for example, P(A ∩ B) is not generally equal to P(A|B); independence does not mean the events are the same; and the joint probability is not simply P(B|A) alone.

Independence means the occurrence of one event does not affect the probability of the other, which is captured by the joint probability P(A ∩ B) = P(A) P(B). Mutual exclusivity means the two events cannot happen at the same time, so their intersection is impossible and P(A ∩ B) = 0. The statement that states both of these precisely names the two distinct relationships: independence uses the product rule, while mutual exclusivity requires a zero intersection. The other options mix up these ideas—for example, P(A ∩ B) is not generally equal to P(A|B); independence does not mean the events are the same; and the joint probability is not simply P(B|A) alone.

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