olymmath

HMMT November 2014 U15

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Carl is on a vertex of a regular pentagon. Every minute, he randomly selects an adjacent vertex (each with probability 12\frac{1}{2} ) and walks along the edge to it. What is the probability that after 10 minutes, he ends up where he had started?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{127}{512}

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