olymmath

HMMT 2008 U5

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A Vandal and a Moderator are editing a Wikipedia article. The article originally is error-free. Each day, the Vandal introduces one new error into the Wikipedia article. At the end of the day, the moderator checks the article and has a 2/32 / 3 chance of catching each individual error still in the article. After 3 days, what is the probability that the article is error-free?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{416}{729}

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