101.One Giant Loop of Spaghetti
★★★classical probabilityHudson River Trading
A plate holds 100 separate strands of spaghetti, so 200 free ends in total. You repeatedly pick two free ends uniformly at random and tie them together, until no free ends remain. What is the probability that the result is a single loop containing all 100 strands?
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At each tie, the only bad event is joining an end to the other end of the very same piece, which closes a loop early. Count how many of the available ends are safe.
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