The Monty Hall problem.

[Whateverist]

Here is a loosely related problem which has fewer distractors.

A bag contains three identical tiles. One is painted with an "X" on both sides. Another is painted with an "O" painted on both sides. The third tile has an "X" painted on one side and an "O" painted on the other.

If you draw a tile and hold it up so that you can only see the side facing you and that side is marked with an "X", what is the probability that the other side is also an "X"?


Correct Solution:

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There are three "X"s you might be seeing. There is an "O" on the back of one of those and an "X" on the back of the other two. So there is a 2/3 chance there is an "X" on the back of the tile you see.

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Popular Incorrect Solution:

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There are two tiles you might be holding up. One of them has an "O" on the other side. The other one has an "X" on the other side. So there is a 1/2 chance there is a an "X" on the back of the tile you see.

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