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What is a Monty Hall problem?

What is a Monty Hall problem? Here are some definitions.

Noun
  1. A brainteaser regarding probability, in which a game show contestant picks a door to win a prize. One door conceals a car; the other two conceal goats. After the contestant picks a door, the host opens one of the two remaining doors which reveals a goat. Counterintuitively, it is then in the contestant's interests to switch to the remaining door.
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