Matching pair from ten differently coloured sock pairs

Question

A drawer holds $10$ pairs of socks, every pair a different colour. You pull out two socks at random. What is the probability they are the same colour?

Short answer

$1/19$ . Whatever the first sock is, only $1$ of the remaining $19$ socks matches it.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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