The calculation we just did is an example of Bayes’ Theorem.9 It provides a logically sound way to avoid inconsistencies between what we thought was true (a positive test means a player uses steroids) and new information that comes our way (half of all players testing positive do not use steroids). Bayes’ Theorem compels us to ask probing questions about what we observe. Instead of asking, “What are the odds that a baseball player uses performance-enhancing drugs?” we ask, “What are the odds that a baseball player uses performance-enhancing drugs given that we know he tested positive for such
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