You see a red side, is the hidden side red too?

Question

Three cards sit in a hat. One is red on both sides, one is black on both sides, and one is red on one side and black on the other. You pull out a card at random and lay it flat on the table. The side facing up is red.

What is the probability the hidden side is also red?

Accepted Answer

The tempting answer is 1/2 (it is either the red-red card or the red-black card), but that ignores which side landed up. Track the six individual card faces instead, since each is equally likely to be the one showing. There are three red faces in the hat: two belong to the red-red card, and one belongs to the red-black card. Seeing a red face means you are equally likely to be looking at any of these three red faces. - Two of those red faces sit on the red-red card, whose hidden side is red. - One of those red faces sits on the red-black card, whose hidden side is black. P(	ext{hidden red} \…

You see a red side, is the hidden side red too?

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