You are on a game show, being asked to choose between three doors. Behind each door, there is either a car or a goat. You choose a door. The host picks one of the other doors, which he knows has a goat behind it, and opens it, showing you the goat. (You know, by the rules of the game, that the host will always reveal a goat.) The host then asks whether you would like to switch your choice of door to the other remaining door. Assuming you prefer having a car more than having a goat, do you choose to switch or not to switch?
Give a complete discussion.
