111.Socks Until a Pair
★★★expected valueJane Street
A drawer holds an unlimited supply of socks in two colours, each sock equally likely to be either colour. You draw socks one at a time until you hold a matching pair. What is the expected number of draws?
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The first draw can never complete a pair. After two draws you either have a pair or one of each — and in the second case the third draw settles it for certain.
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