The painted cards

Question

A hat contains 3 cards. Two of them are painted white on both sides. The third is painted white on one side and black on the other. You draw a card at random and lay it down so you can see one face: it is white.

What is the probability that the hidden side of that card is also white?

Accepted Answer

Condition on the face you are actually looking at. Count all the white faces in the hat, since seeing white means you are equally likely to be looking at any one of them. - Each of the 2 double-white cards has 2 white faces, giving 4 white faces. - The mixed card has 1 white face. That is 5 equally likely white faces in total. For 4 of them (the ones on double-white cards) the reverse side is white; for the remaining 1 (the white side of the mixed card) the reverse is black. So P(	ext{other side white} \mid 	ext{seeing white}) = \frac{4}{5}. The naive "it is one of two cards, so 	frac{1}{2…

The painted cards

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