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I divide my email into three categories: A1 = spam. A2 = low priority, A3 = high priority. I find that: P(A1) = .7 P(A2) = .2 P(A3) = .1 Let B be the event that an email contains the word "free". P(B|A1) = .9 P(B|A2) = .01 P(B|A3) = .01 I receive an email with the word "free". What is the probability that it is spam?
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