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Fall 2011 Strategic Practice 2: Section 3 (Thinking Conditionally) - Question 2
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A spam filter is designed by looking at commonly occurring phrases in spam. Suppose that 80% of email is spam. In 10% of the spam emails, the phrase "free money" is used, whereas this phrase is only used in 1% of non-spam emails. A new email has just arrived, which does mention "free money". What is the probability that it is spam?

Solution: Let S be the event that an email is spam and F be the event that an email has the "free money" phrase. By Bayes' Rule, P(S|F) = 80/82.