Today at Not About Apples, I give my take on what might be the most confusing and misunderstood (certainly the most fistfight-inducing) probability question in history: the Monty Hall problem.
As I tell it, this is the story of the following scripted game. The characters are Alice (the contestant) and Hatter (the host).
Monty Hall Setup
There are three doors. One leads to a car, and the other two lead to goats. (The locations of the car and the goats are assigned at random in advance, and Hatter is aware of what is where.)
Alice chooses one door (which she hopes leads to the car) but does not open it.
Hatter, knowing where the car is, opens one of the doors that Alice did not choose, showing her a goat. (That is, if she picked a goat, he’ll show her the other goat; if she picked the car, he’ll arbitrarily choose a goat to show her.)
Now there are two doors, and Alice knows for sure that one leads to a car and one leads to a goat. Hatter then offers Alice the option to either switch her choice to the other door or stick with the door she had chosen at the start.
Assuming that Alice wants a car and doesn’t want a goat, is it in her interest to take the prize behind her original door, or is it in her interest to take the prize behind the other door, or does it not matter?
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