HMMT 2015 C2
- Combinatorics
- Answer
Victor has a drawer with 6 socks of 3 different types: 2 complex socks, 2 synthetic socks, and 2 trigonometric socks. He repeatedly draws 2 socks at a time from the drawer at random, and stops if the socks are of the same type. However, Victor is "synthetic-complex type-blind", so he also stops if he sees a synthetic and a complex sock.
What is the probability that Victor stops with 2 socks of the same type? Assume Victor returns both socks to the drawer after each step.
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{3}{7}
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