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What is the expected number of loops (strings tied to their own end)?

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You have a bag with 'N' strings in it. You randomly grab two ends and tie them together until there are no more loose ends.

In the end, what is the expected number of loops (strings tied to their own end)?

posted Jan 9, 2015 by Ankur Athari

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1 Answer

+1 vote

1 + 1/3 + 1/5 ... + 1/(2N-1).

Each time you tie two together the number of string ends available decreases by 2. The chance of grabbing a string and its end is 1/(2N-1).

answer Aug 19, 2015 by Anamika



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