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Homework 1: The Monty Hall Problem

You're on a game show hosted by Monty Hall. There are three doors: behind
one door is a new car (Monty Hall knows exactly which door has the car).
You are asked to pick a door. Then, Monty Hall opens one of the other two
doors to show you that there is no car behind it (remember that
he knows exactly which door has the car). Monty then gives you the choice
of either staying with your original choice or switching your choice to
the remaining door.
What should you do? Does it matter?

Professor Edwin Chong,