Monty Hall problem

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Here's a favorite interesting probability problem.

Suppose you are on Monty Hall's "Let's Make a Deal!".  You are given the choice of three doors, behind one door is a car, the others, goats.  You pick a door, say 1, Monty opens another door, say 3, which has a goat.  Monty says to you "Do you want to pick door 2?"  Is it to your advantage to switch your choice of doors?

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关键词：problem Monty Hall mont Rob Hall problem Monty

Here's a variation of the Monty Hall problem:

What if Monty forgot which door has the car behind it.  He makes a guess at which of the two doors to open and gets lucky, opening a door behind which stands a goat.  Now would you switch?

Yes, definitely.