Matching pair from a drawer with one odd triple

Question

A drawer contains $21$ socks in $10$ colours: nine colours have exactly two socks each, and the tenth colour has three. Two socks are taken out at random. What is the probability that they are the same colour?

Short answer

$2/35$ . Of the $\binom{21}{2}=210$ possible pairs, the matching ones are the $9$ two-sock colours plus $\binom32=3$ from the three-sock colour, so $12/210=2/35$ .

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

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Lessons behind this question

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

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