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Socks in the dark

It's dark, and your drawer holds 10 pairs of socks, every pair different: 20 socks in all. You pull socks out one at a time at random until two of them make a matching pair. How many socks do you expect to pull?

Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.

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