We think that getting more information about a situation helps us make more accurate predictions. There are times, though, when some well-chosen information can wreck our rationality. All we need is a good stereotype.
This phenomenon was first explored in Judgment Under Uncertainty: Heuristics and Biases. Heuristics are mental rules of thumb, little tricks and strategies we use to solve mental problems. Sometimes these are helpful; other times, they lead us astray. The writers of the paper, Daniel Kahneman and Amos Tversky, demonstrated this when they asked subjects to identify a person's profession after a short description of that person's character. For example, they told people about a man who was neat, meticulous, good-hearted, but not social, and asked the people if he was a librarian or a farmer. The subjects tended to think the man was a librarian, judging that these characteristics were more suited to a librarian than a farmer. That might be true, but Kahneman and Tversky pointed out that there were 20 male farmers in the United States for every male librarian. The stereotype would have to be overwhelmingly true of librarians and false for farmers for a male subject, picked at random, to more likely be a librarian than a farmer.
The stereotype fake-out pops up again in the conjunction fallacy. To demonstrate this particular fallacy a similar procedure is used. Subjects are given an assessment of a person's character and then asked to rank statements about them in terms of likelihood. The famous example is Linda: Linda is outspoken, smart, single, and she was politically active in college, focusing on discrimination, social justice, and nuclear proliferation. The statements about her included things like, "Linda is an elementary school teacher," and "Linda works in a bookstore and takes yoga," but the statements researchers were particularly interested in were, "Linda is a bank teller," and "Linda is a bank teller and is active in the feminist movement." The bank teller with a feminist qualification statement was almost always ranked as more likely than the simple bank teller statement. Although almost everyone in college is at some point politically active, although there are far fewer bank tellers who are active in the feminist movement than overall bank tellers, and although the simple bank teller statement doesn't preclude Linda from being a feminist as well as a bank teller, people thought the qualified statement was more likely.
This was emphasized when 57% of participants in the study ranked the feminist statement as more likely than the statement, "Linda is a bank teller whether or not she is active in the feminist movement." Even when explicitly told that the "feminist" variant of the statement was a smaller category within the "bank teller" statement, people still believed that the subcategory was more likely. And why? Well, if she's bright, outspoken, and single, she sounds like a feminist more than anything else, even if that's impossible. Qualifications always make a category more specific and less likely to apply to an individual, but when people fit our mental picture of what a subcategory "should" be, the actual odds don't matter.