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?

Show hints (2)+

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

Answer

Reveal answer →

0.0526 (± 0.001)

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: IMC, Flow Traders

Drawing a matching pair of socks

Answer

Related questions