Explain conditional probability and independence in everyday language and situations.
Evaluate a real-world conditional probability claim
Problem
Is this real-world probability claim stated correctly? \(80\%\) of positive tests mean \(80\%\) of people with positive tests have the disease, but the statistic was \(P(\text{positive}|\text{disease})\).
Big Picture
What this problem is really about
Reversing a conditional changes its reference group and generally changes its value. We’ll interpret the supplied disease-conditioned test rate, write the positive-test-conditioned claim separately, compare their denominators, and identify prevalence and false-positive behavior as missing information needed for the reversed probability.
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