2023 AMC 12B Problems/Problem 20
Solution
Denote by 
the position after the 
th jump.
Thus, to fall into the region centered at 
and with radius 1, 
.
Therefore, the probability is
![\[ \frac{2 \cdot 2 \arcsin \frac{1}{4}}{2 \pi} = \boxed{\textbf{(E) } \frac{2 \arcsin \frac{1}{4}}{\pi}}. \]](http://latex.artofproblemsolving.com/6/e/d/6edb5c671433291b14a0e16f099947181f8a4717.png)
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
