olymmath

HMMT 2003 U42

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A tightrope walker stands in the center of a rope of length 32 meters. Every minute she walks forward one meter with probability 3/43 / 4 and backward one meter with probability 1/41 / 4. What is the probability that she reaches the end in front of her before the end behind her?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3^{16}}{3^{16}+1}

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