Compute conditional probability as the fraction of one event's outcomes that also belong to another event.
Find the given-event total from a joint count and a conditional probability
Problem
Solve \(P(A|B)=\text{joint}~\text{count}/\text{condition}~\text{total}\) for the condition total when the joint count is \(18\) and \(P(A|B)=0.60\).
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What this problem is really about
When the joint count and conditional rate are known, the conditioned-group total is the unknown denominator. We’ll write the rate equation, clear that denominator, divide the known joint count by the rate, and check both that the recovered total exceeds the part and recreates the original fraction.
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