Compute conditional probability as the fraction of one event's outcomes that also belong to another event.
Find a joint count from a conditional probability and a given condition count
Problem
Use \(\text{joint}~\text{count}~=~P(A|B)~\times~B~\text{count}\) to calculate the overlap when \(P(A|B)=0.40\) and the \(B\) count is \(50\).
Big Picture
What this problem is really about
A conditional rate times its conditioned-group count recovers the joint count. We’ll rearrange the favorable-over-group relationship, multiply the rate by the B total, check that the result is a whole count within the group, and divide back to verify the conditional probability.
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