The New York Times has an article today about how a logical fallacy may have distorted results in what social scientists call cognitive dissonance. I won't get into what cognitive dissonance is, but the logical fallacy is based on something mathematicians call the Monty Hall Problem.
You are a contestant on the game show Let's Make a Deal. There are three doors. Behind one of them is a new car and behind the other two, goats. You pick a door but before it opens, Monty opens one of the other two doors to reveal a goat. Monty then gives you the chance to switch doors. If you want the car rather than the goat, what should you do? Stay or switch?
Switch! You might think choosing between two doors gives you 50-50 odds, but you'd be wrong. Before the first door opened, you had a 1 in 3 chance of winning. Once the door is opened, you'll win every time your original guess was wrong, which it would have been 2 out of 3 times.
If you don't believe me, you can go to the Monty Hall Problem at the NYTimes, play the game, and prove it to yourself. The site will keep track of statistics for you.