MathDB
AMELIA ATEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Source: 2022 AMC 10B #23 / 2022 AMC 12B #22

November 17, 2022
AMCAMC 10AMC 122022 AMC2022 AMC 10B2022 AMC 12B

Problem Statement

Ant Amelia starts on the number line at 00 and crawls in the following manner. For n=1,2,3,n=1,2,3, Amelia chooses a time duration tnt_n and an increment xnx_n independently and uniformly at random from the interval (0,1).(0,1). During the nnth step of the process, Amelia moves xnx_n units in the positive direction, using up tnt_n minutes. If the total elapsed time has exceeded 11 minute during the nnth step, she stops at the end of that step; otherwise, she continues with the next step, taking at most 33 steps in all. What is the probability that Amelia’s position when she stops will be greater than 11?
<spanclass=′latex−bold′>(A)</span>13<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>34<spanclass=′latex−bold′>(E)</span>56<span class='latex-bold'>(A) </span>\frac{1}{3} \qquad <span class='latex-bold'>(B) </span>\frac{1}{2} \qquad <span class='latex-bold'>(C) </span>\frac{2}{3} \qquad <span class='latex-bold'>(D) </span>\frac{3}{4} \qquad <span class='latex-bold'>(E) </span>\frac{5}{6}
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