Difference between revisions of "2023 AMC 12B Problems/Problem 20"
(Created page with "==Solution== Denote by <math>A_i</math> the position after the <math>i</math>th jump. Thus, to fall into the region centered at <math>A_0</math> and with radius 1, <math>\ang...") |
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Therefore, the probability is | Therefore, the probability is | ||
| − | < | + | <cmath> |
\[ | \[ | ||
\frac{2 \cdot 2 \arcsin \frac{1}{4}}{2 \pi} | \frac{2 \cdot 2 \arcsin \frac{1}{4}}{2 \pi} | ||
| − | = \boxed{\textbf{(E) | + | = \boxed{\textbf{(E) } \frac{2 \arcsin \frac{1}{4}}{\pi}}. |
\] | \] | ||
| − | + | </cmath> | |
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
Revision as of 18:38, 15 November 2023
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)
