Which expression correctly defines P(A|B)?

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Multiple Choice

Which expression correctly defines P(A|B)?

Explanation:
Conditional probability asks: what is the chance that A happens when we already know B has occurred? It is defined as the probability that both A and B occur, divided by the probability that B occurs, provided B has positive probability. So the expression that matches is the ratio P(A∩B) / P(B), with the condition P(B) > 0. Think of narrowing the sample space to the outcomes where B happens, and then asking what fraction of those outcomes also have A. If you tried to use P(B|A), you’d be measuring the chance of B given A, which is a different condition. Subtracting probabilities or taking the union of A and B doesn’t reflect conditioning either.

Conditional probability asks: what is the chance that A happens when we already know B has occurred? It is defined as the probability that both A and B occur, divided by the probability that B occurs, provided B has positive probability. So the expression that matches is the ratio P(A∩B) / P(B), with the condition P(B) > 0.

Think of narrowing the sample space to the outcomes where B happens, and then asking what fraction of those outcomes also have A. If you tried to use P(B|A), you’d be measuring the chance of B given A, which is a different condition. Subtracting probabilities or taking the union of A and B doesn’t reflect conditioning either.

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