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Question: There are 16 disks in a box. Five of them are painted red, five of them are painted blue, and six are painted red on one side, and blue on the other side. We are given a disk at random, and see that one of its sides is red. Is the other side of this disk more likely to be red or blue?

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    To fully specify the problem, you need to specify how we see that one of the sides is red. The answer would be different if a) we randomly choose a side to look at or b) we can somehow tell (e.g. by looking from a distance) whether one of the sides of a disk is red or not or c) the person who drew the disk gives it to us with a red side showing, possibly according to some strategy such as always showing a red side if possible.2012-04-09
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    @joriki : "We are given a disk at random, and see that one of its sides is red" is enough for me to believe that I am given a random disk and I see a random side of the disk? I don't think we should over exaggerate over this.2012-04-09
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    @Patrick: I agree. The problem would be if we were _told_ that one of its sides was red -- then we would be in Monty Hall territory.2012-04-09
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    @Patrick: I think it likely that yours is the intended interpretation $-$ that we are equally likely to see each of the $32$ sides $-$ but I also think that it’s important for the OP to understand **why** we need to make some assumption here.2012-04-09
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    @Brian M.Scott : OP gave the combinatorics tag, so I expected he wanted it to be a combinatorics problem, which doesn't fit with the game-theoretic possibilities. I didn't wanna bother the OP.2012-04-09
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    "probabilistic method" has a different meaning and I removed it from the title. Also added probability tag.2012-04-09

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