I show you three cards. One is white on both sides, one is black on both sides, and one is white on one side and black on the other. I shake them in a hat, remove one at random, and place it on a table. The side that’s face up is black. What’s the probability that the other side is also black?
Hint: It’s not 1/2.
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The probability is 2/3 that the other side is also black.
There are six faces. Of the three black faces, 2/3 are on the black/black card. So if you’re presented with a black face, chances are 2 in 3 that it’s on the black/black card — and thus that the card’s other side is black.
See also Boy Trouble and The Monty Hall Problem.
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