Cricket Random Hop Probability

1800SpecialistCombinatoricsProbability

AMC 8 · 2022 · Problem 25

A cricket randomly hops between $4$ leaves, on each turn hopping to one of the other $3$ leaves with equal probability. After $4$ hops, what is the probability that the cricket has returned to the leaf where it started? [[File:2022 AMC 8 Problem 25 Picture.jpg|center|600px]]

Answer choices

\frac{2}{9}

\frac{19}{80}

\frac{20}{81}

\frac{1}{4}

\frac{7}{27}

0 students attempted0% solvedRating 1800

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