If two events A and B are independent, how does P(A and B) relate to P(A) and P(B)?

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Multiple Choice

If two events A and B are independent, how does P(A and B) relate to P(A) and P(B)?

Explanation:
Independence means the occurrence of one event doesn’t affect the likelihood of the other. When that’s the case, the chance that both events happen is the product of their individual chances. So P(A and B) equals P(A) × P(B). For example, if each event has probability 0.5, the joint probability is 0.25. The other expressions aren’t about the joint occurrence: adding would mix probabilities in a way that doesn’t reflect both occurring together, P(A|B) is the conditional probability of A given B and isn’t generally equal to P(A) unless you’re explicitly stating independence, and subtracting probabilities isn’t how you combine them to get the join.

Independence means the occurrence of one event doesn’t affect the likelihood of the other. When that’s the case, the chance that both events happen is the product of their individual chances. So P(A and B) equals P(A) × P(B). For example, if each event has probability 0.5, the joint probability is 0.25. The other expressions aren’t about the joint occurrence: adding would mix probabilities in a way that doesn’t reflect both occurring together, P(A|B) is the conditional probability of A given B and isn’t generally equal to P(A) unless you’re explicitly stating independence, and subtracting probabilities isn’t how you combine them to get the join.

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