P(A|B) is equal to which expression?

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Multiple Choice

P(A|B) is equal to which expression?

Conditional probability asks for the probability of A given that B has occurred. It is defined as the probability of A and B both happening divided by the probability that B occurs, provided P(B) > 0. This reflects restricting attention to outcomes in B and asks what portion of that B-portion also lies in A. So P(A|B) = P(A ∩ B) / P(B). The other forms aren’t correct: P(B)/P(A) is the reverse, P(A ∪ B)/P(B) uses the union, and P(A)P(B) would only equal P(A|B) if A and B were independent.

Conditional probability asks for the probability of A given that B has occurred. It is defined as the probability of A and B both happening divided by the probability that B occurs, provided P(B) > 0. This reflects restricting attention to outcomes in B and asks what portion of that B-portion also lies in A. So P(A|B) = P(A ∩ B) / P(B). The other forms aren’t correct: P(B)/P(A) is the reverse, P(A ∪ B)/P(B) uses the union, and P(A)P(B) would only equal P(A|B) if A and B were independent.

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