There was an old TV game show called "Let's Make a Deal" where the contestants would dress in funny costumes and try to win prizes from the host Monty Hall. You are a contestant on this show and Monty says you will win the prize behind whichever one of three closed doors you pick. He tells you that two of the doors have a goat hidden behind them and the third door hides a new car. Obviously, you would rather win the car. You pick one of the doors and Monty says: "Before I show you what is behind the door you picked, I want to show you what's behind one of the doors you didn't pick." He opens one of the other doors and reveals a goat. Now he says: "Before I show you what you won, I will give you a chance to change your choice and switch to the other closed door, if you want." Should you take Monty up on his offer and switch? Why, or why not