[Verse 1] Sarah's screening mammograms, testing for disease One percent have cancer, that's the frequency we see Test detects ninety percent when cancer's really there But false alarms happen, five percent who are clear [Chorus] Prior times likelihood, divided by the whole That's Bayes in action, updating what we know Posterior probability, the answer we seek New evidence reshapes what the numbers speak [Verse 2] Started with one percent, our prior belief intact Positive test result, now what's the actual fact? Don't jump to conclusions, the math will show the way Point-oh-nine times point-oh-one, numerator's in play [Chorus] Prior times likelihood, divided by the whole That's Bayes in action, updating what we know Posterior probability, the answer we seek New evidence reshapes what the numbers speak [Bridge] Total probability, partition the space complete All possible pathways, every route we meet Cancer times detection, plus healthy times mistake Point-oh-oh-nine plus point-oh-four-nine-five, denominator we make [Verse 3] Point-oh-oh-oh-nine divided by point-oh-five-oh-four Fifteen point five percent, not ninety like before Base rates matter deeply, they anchor what we find Rare events stay rare, even with tests combined [Chorus] Prior times likelihood, divided by the whole That's Bayes in action, updating what we know Posterior probability, the answer we seek New evidence reshapes what the numbers speak [Outro] Investment decisions, credit risk assessment too Bayes guides our judgment when the data's coming through Update your beliefs with every signal that arrives That's how probability in finance comes alive
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