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2023 AMC 12B Question 20

AMC12 · 2023 AMC 12B

Question 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?
  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{5}$
  3. $\dfrac{\sqrt{3}}{8}$
  4. $\dfrac{\arctan\tfrac12}{\pi}$
  5. $\dfrac{2\arcsin\tfrac14}{\pi}$