HMMT November 2023 E1
- General
- Answer
Four people are playing rock-paper-scissors. They each play one of the three options (rock, paper, or scissors) independently at random, with equal probability of each choice. Compute the probability that someone beats everyone else. (In rock-paper-scissors, a player that plays rock beats a player that plays scissors, a player that plays paper beats a player that plays rock, and a player that plays scissors beats a player that plays paper.)
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{4}{27}
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