An articlein www.networkworld.com about evaluating email filters that are designed to detect spam described a test of MailFrontier's Anti-Spam Gateway (ASG). In the test, there were 7840 spam mes- sages, of which ASG caught 7005. Of the 7053 messages that ASG identified as spam, they were correct in all but 48 cases.

1. 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.
2. For this test, given that a message is truly spam, esti- mate the probability that ASG correctly detects it.
3. Given that ASG identifies a message as spam, estimate the probability that the message truly was spam.