Here's a simplified look at a spam filter algorithm... We are worried about the phrase "make money fast" and our IT team has figured that P ("make money fast"|junk mail) = 0.20 and P ("make money fast"|NOT junk mail) = 0.001 In addition they figured that half of our emails is junk. 1. What is the marginal probability of seeing "make money fast" in a message? In other words, what is the P ("make money fast")? 2. If the spam filter always classify a message containing "make money fast" as junk, how often will it make a mistake? In other words, what is the P (NOT junk mail|"make money fast") ? 3