# Question

Because of the increasing nuisance of spam e-mail messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 95% accurate. The way the advertisement is worded, 95% accurate could mean that (a) 95% of spam is blocked, (b) 95% of valid e-mail is allowed through, (c) 95% of the e-mail allowed through is valid, or (d) 95% of the blocked e-mail is spam. Let S denote {message is spam}, and let B denote {filter blocks message}. Using these events and their complements, identify each of these four possibilities as a conditional probability.

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