Consider the Monty Hall problem, except that there are
5 doors (4 contain goats and 1 contains a car). After the contestant has selected a door, Monty reveals
goats behind 3 other doors and offers you the chance to switch to the remaining door.
Assume that Monty knows which door has the car, will always open 3 goat doors, and that Monty
chooses with equal probabilities from all choices of which goat doors to open. Should you switch doors?
What is the probability of winning a car if you switch?