Let's say you are a contestant on a game show. The host of the show presents you with a choice of 4 doors, which we will call doors 1, 2, 3, and 4. You do not know what is behind each door, but you do know that a new Cadillac Escalade and 3 old cars are randomly placed behind the doors. The host knows where the Escalade is. The game is played out is as follows. The host lets you choose a door. The host opens a door with an old car and asks you whether or not you want to change your door choice. a