An article on www.networkworld.com about evaluating e-mail filters that are designed to detect spam described a test of MailFrontier 's Anti-Spam Gateway (ASG). In the test, there were 7840 spam messages, of which ASG caught 7005. Of the 7053 messages that ASG identified as spam , they were correct in all but 48 cases.
a. Set up a contingency table that cross classifies the actual spam status (with the rows "spam " and " not spam ") by the ASG filter prediction (with the columns " predict message is spam" and " predict message is not spam"). Using the information given, enter counts in three of the four cells.
b. For this test, given that a message is truly spam, estimate the pr obability that ASG correctly detects it.
c. Given that ASG identifies a message as spam, estimate the probability that the message truly was spam.