You are a contestant in the game show "Let's make a Deal." In this game show, there are three curtains. Behind one of the curtains is a new car, and behind the other two are cans of spam. You get to pick one of the curtains. After you pick that curtain, the emcee, Monte Hall, who we assume knows where the car is, reveals what is behind one of the curtains that you did not pick, showing you some cans of spam. He then asks you if you would like to switch your choice of curtain. Should you switch? Why or why not? Please answer this question carefully. You have all the tools needed to answer it, but several math Ph.D.'s are on record (in Parade Magazine) giving the wrong answer.