If I ever taught probability and statistics, this is the problem I'd put on the board the first lecture:
Colin comes up to Barry and Frank and says, "hey guys! I have a coin here which is biased but I won't tell you which way or by how much. What's the probability of the next toss being tails?". Barry replied, "given what we know, it is 0.5". Frank looked astonished. "How can you say 0.5? Given the coin is biased, that's the one probability we know it can't be." Who is right, Barry or Frank?
UPDATE: corrected "a tail" to "tails".
UPDATE 2: Eliezer Yudkowsky has a great post on exactly this scenario. He's way smarter than I, so go read him :-)
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