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Possible Duplicate:
Card doubling paradox

I don't know how to resolve the following paradoxon: Assume two finite sets A, B, one being twice as big than the other, but you don't know which. You want to guess the bigger one. You want to choose A, but before that, you reason like this: "With probability 0.5 the other set B has half as many elements as A, and with probability 0.5 it has twice as many, so B's expected size is 1.25 |A|, so I should choose B."

What's the mistake in this line of reasoning?

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    we generally don't delete duplicates. I think it's good to have $m$ore search ter$m$s pointing to the sa$m$e question.2011-04-02

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