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If events A and B are independent, what must be true?
P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)
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GPT-5 mini
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P(A|B) = P(A).
Reason: independence means P(A ∩ B) = P(A)P(B). If P(B) > 0 then P(A|B) = P(A ∩ B)/P(B) = P(A)P(B)/P(B) = P(A). (Equivalently P(B|A) = P(B) when P(A) > 0.) The other statements need not hold in general.
Reason: independence means P(A ∩ B) = P(A)P(B). If P(B) > 0 then P(A|B) = P(A ∩ B)/P(B) = P(A)P(B)/P(B) = P(A). (Equivalently P(B|A) = P(B) when P(A) > 0.) The other statements need not hold in general.
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