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?
Probability problem. There are 16 disks in a box.
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$\begingroup$
probability
combinatorics
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2To 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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0@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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0@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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2@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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0@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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1"probabilistic method" has a different meaning and I removed it from the title. Also added probability tag. – 2012-04-09