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HMMT November 2022 T4

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You start with a single piece of chalk of length 1. Every second, you choose a piece of chalk that you have uniformly at random and break it in half. You continue this until you have 8 pieces of chalk. What is the probability that they all have length 18\frac{1}{8} ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{63}

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