5.29 Spam 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 adver-
tised 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.