Drawing a matching pair of socks

EasyProbability Combinatorics~2m

A drawer holds $10$ pairs of socks, each pair a distinct color ( $20$ socks total). You pull out $2$ socks at random. What is the probability they form a matching (same-color) pair?

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Fix the first sock; how many of the remaining $19$ socks match its color?
Exactly one, so the probability is $\tfrac{1}{19}$ . (Check: $\tfrac{10}{\binom{20}{2}}=\tfrac{10}{190}$ .)

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0.0526 (± 0.001)

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Drawing a matching pair of socks

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