I was reminded of this homework problem that I give my students as I was riding in on the F train this morning. It is a very good problem because it is exceedingly simple and nicely demonstrates two problems of the classical way of looking at statistics.
All you need to do this homework is a busy place and some free time, about 20 minutes.
Find a spot where people congregate or pass by. Be sure to carefully and concretely specify this place: keep its boundaries fixed and rigid for the duration of the homework.
Count the people in the spot, either all at once, or as they pass by for some fixed time (decided in advance). Also count the number of people who are wearing some sort of thinking-suppression device. There are obviously any number of other things you can take note of, like sex, age, etc., but we’ll ignore all of them.
Report back to me (in the Comments) the two numbers, number wearing thinking-suppression devices, which will be less than or equal to the total number of people. Also note details of your spot.
We are obviously going to be talking about forming ratios and estimating probabilities. I’ll discuss what all this means–and what it does not mean—once a few people have turned in the assignment.
Oh, yes. A thinking-suppression device is anything like an I-Pod, MP3 player, etc. etc.