314.Ramen Noodle Loops
★★★expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability
There are 100 noodles in your bowl of ramen. You repeatedly pick two loose ends uniformly at random and connect them, until no loose ends remain. On average how many circles (loops) do you create? Round to the nearest hundredth.
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At each connection, what is the probability you close a loop, given how many loose ends remain? Then use linearity.
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