Tuesday, November 20, 2007

Consider this problem. You are running a high school and you suspect some gang activities, so you want to be on the lookout for people wearing gang `uniforms'. But you don't know what any of the uniforms might be. So you watch the students and take note of what they are wearing: some have puffy jackets, some have hoodies, some have t-shirts, some have baggy pants, some have hats that they wear backwards, etc. etc. etc. Over the course of the day, you see a lot of different clothing, a lot of different combinations, and all in different colors. You note, however, that you did see five students wearing purple puffy jackets, baggy pants, and red baseball caps. What is the liklihood that this is a gang uniform? Obviously, it will depend on the size of the student population and the prevalence of certain kinds of clothing, but in the extreme case where you see, say, fifteen students with the *exact* same outfits that match in twenty-seven different random qualities, you can be pretty sure that is a gang. On the other hand, if you see two students that happen to wear the same color puffy jacket and otherwise have nothing in common, you can write that one off as coincidence. So given the number of students and the relative prevalence of various clothing elements, how many points of coincidence do you need to be fairly certain you have found a gang uniform?