Question
Suppose that you are a contestant on a game show and you have to choose between n closed doors. Whatever is behind that door is
Suppose that you are a contestant on a game show and you have to choose between
n closed doors. Whatever is behind that door is your prize. Behind one door is a brand new car
(which is what you would like to have) and behind the other n - 1 doors are goats. The host of
the show, Monty, knows where the car and goats are located, but you, being the contestant, does
not. Suppose you pick a door at random. Before Monty opens the door you chose, he randomly
opens k doors such that each of the k doors have a goat behind it, where 0 k n - 2. (Note
that he never opens the door with the car during this process). He then asks you if you would
like to switch your door to any of the remaining doors. Should you choose to switch your door,
you randomly select any of the remaining doors. If you decide to switch your door, what is the
probability that you win the car?
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