HMMT 2017 C6
- Combinatorics
- Answer
Emily starts with an empty bucket. Every second, she either adds a stone to the bucket or removes a stone from the bucket, each with probability . If she wants to remove a stone from the bucket and the bucket is currently empty, she merely does nothing for that second (still with probability ). What is the probability that after 2017 seconds her bucket contains exactly 1337 stones?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{\left(\begin{array}{l}2017 \ 340\end{array}\right)}{2^{2017}}
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