Donald Jones is either a librarian or a salesman. His personality can best be described as retiring. What are the odds that he is a librarian?
When we use this little problem in seminars, the typical response goes something like this: “Oh, it’s pretty clear that he’s a librarian. It’s much more likely that a librarian will be retiring; salesmen usually have outgoing personalities. The odds that he’s a librarian must be at least 90 percent.” Sounds good, but it’s totally wrong.
The trouble with this logic is that it neglects to consider that there are far more salesmen than male librarians. In fact, in the United States, salesmen outnumber male librarians 100 to 1. Before you even considered the fact that Donald Jones is “retiring,” therefore, you should have assigned only a 1 percent chance that Jones is a librarian. That is the base rate.
Now, consider the characteristic “retiring.” Suppose half of all male librarians are retiring, whereas only 5 percent of salesmen are. That works out to 10 retiring salesmen for every retiring librarian — making the odds that Jones is a librarian closer to 10 percent than to 90 percent. Ignoring the base rate can lead you wildly astray.
