HMMT 2010 C9
- Combinatorics
- Answer
Rosencrantz and Guildenstern are playing a game where they repeatedly flip coins. Rosencrantz wins if 1 heads followed by 2009 tails appears. Guildenstern wins if 2010 heads come in a row. They will flip coins until someone wins. What is the probability that Rosencrantz wins?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{2^{2009}-1}{3 \cdot 2^{2008}-1}
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