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HMMT 2024 U2

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Jerry and Neil have a 3 -sided die that rolls the numbers 1,2 , and 3 , each with probability 13\frac{1}{3}. Jerry rolls first, then Neil rolls the die repeatedly until his number is at least as large as Jerry's. Compute the probability that Neil's final number is 3 .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{11}{18}

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