Cyrus Frog 2-Unit Jump Random

1800SpecialistCombinatoricsProbability

AMC 12B · 2023 · Problem 20

Cyrus the frog jumps $2$ units in a direction, then $2$ more in another direction. What is the probability that he lands less than $1$ unit away from his starting position?

Answer choices

~\frac{1}{6}

~\frac{1}{5}

~\frac{\sqrt{3}}{8}

~\frac{\arctan \frac{1}{2}}{\pi}

~\frac{2\arcsin \frac{1}{4}}{\pi}

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