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2022 AMC 10B Problem 23

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2022 AMC 10B Problem 23AMC 10 Step by Step
Name:                             Date: September 13, 2026
Geometric Probability · difficulty 4 of 5 · about 6 min · position P21-25

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 nn th 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 nn th 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 ?

  1. A)

    13\frac{1}{3}

  2. B)

    12\frac{1}{2}

  3. C)

    23\frac{2}{3}

  4. D)

    34\frac{3}{4}

  5. E)

    56\frac{5}{6}

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