Understand conditional probability and connect independence to unchanged conditional probabilities.
Find \(P(A \mid B)\) from counts by dividing within the conditioned group
Problem
Using the diagram, calculate \(P(A|B)\) from the \(A\cap{}B\) count \(8\) and the conditioned \(B\) count \(20\). Do not divide by the overall total \(50\).
Conditioning replaces the full sample space with the outcomes inside the named event. We’ll use the count in B as the new denominator, use the overlap of A and B as the favorable count, and reduce their ratio. Checking that the denominator is not the overall total confirms that the reference group was narrowed correctly.
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