If A and B are independent, which statement is true?

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Multiple Choice

If A and B are independent, which statement is true?

Explanation:
Independence means knowing B happened doesn’t change the likelihood of A. The conditional probability P(A|B) is defined as P(A ∩ B) / P(B) (assuming P(B) > 0). If A and B are independent, then P(A ∩ B) = P(A)P(B). Substituting gives P(A|B) = [P(A)P(B)] / P(B) = P(A). So the probability of A given B is just the probability of A.

Independence means knowing B happened doesn’t change the likelihood of A. The conditional probability P(A|B) is defined as P(A ∩ B) / P(B) (assuming P(B) > 0). If A and B are independent, then P(A ∩ B) = P(A)P(B). Substituting gives P(A|B) = [P(A)P(B)] / P(B) = P(A). So the probability of A given B is just the probability of A.

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