The Monty Hall Problem

This puzzle is based on a common situation from Let’s Make a Deal. The player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door revealing a goat. The host then offers the player an option to switch to the other closed door. Does switching improve the player’s chance of winning the car?

Beaudry and I have discussed this many times, and I think we finally sort of understand the answer. Here’s the explanation, thanks to Wikipedia, which has to be on the top 10 most useful websites.

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