AP Statistics / Mr. Hansen
11/29/1999

You are a contestant on a TV game show [the camp 1960s and 70s classic, Let’s Make a Deal], and the host, Monty Hall, offers you a choice of Door #1, Door #2, or Door #3. However, one difference from the real TV show, which often became a mind game, is that you are told in advance that after you choose, a blank door will be revealed and you will be offered the option of switching your choice.

Only one door conceals a prize; the other two are blank. [Actually, in the TV show, behind the two non-winning doors would be "junk" prizes such as an old clunker car or a goat.] You choose a door, and Monty reveals one of the other doors to be blank. What is the probability that your original door is the winning door? More to the point, should you keep your original door, or should you switch?