Consider the following simplified version of the television game show Let's Make a Deal. There is a grand prize behind one of three curtains; the other two curtains are empty. As a contestant, you get to choose a curtain at random. Let's say you choose curtain 3. Before revealing what's behind the curtain, the game show host always offers to show you what one of the other curtains contains. She shows you that curtain 2 is empty; in fact, she always shows you an empty curtain. (You know that's how the game works; so do the audience and everybody else.) Now you must decide: Do you stick with your original choice, curtain 3, or switch to curtain 1? Which action gives you the better chance of finding the grand prize?