Question
A Naive Bayes spam filter has priors P(Spam)=0.4 and P(Ham)=0.6. For an email containing the word "free", the likelihoods are P("free"|Spam)=0.7 and P("free"|Ham)=0.1. Using Bayes' theorem, what is P(Spam | "free"), the posterior probability that the email is spam?
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