You are a contestant on the classic "let's make a deal" game show.
You are confronted with three closed (and opaque) doors. Behind one of the doors is a new car. Behind the other two doors are goats.
You choose one of the doors at random. Monty Hall, the show's host, then reveals what is behind one of the other doors. He knows which door has the car, and always opens a door which has a goat behind it.
He then asks you if you would like to change your choice of door. Assuming you would prefer a car to a goat, you will not choose the door he just opened. But should you switch to the other closed door?
Estimate the probability that you will win the car if you stay with your original door, and the probability that you will win the car if you switch. Should it make any difference?