AMC 10 Step by Step
Log inSign up
Printable

2023 AMC 10B Problem 19

Include the solutionBack to the problem
2023 AMC 10B Problem 19AMC 10 Step by Step
Name:                             Date: September 13, 2026
Geometric Probability · difficulty 3 of 5 · about 4 min · position P16-20

Sonya the frog chooses a point uniformly at random lying within the square [0,6][0, 6] ×\times [0,6][0, 6] in the coordinate plane and hops to that point. She then randomly chooses a distance uniformly at random from [0,1][0, 1] and a direction uniformly at random from {north, south, east, west}. All her choices are independent. She now hops the distance in the chosen direction. What is the probability that she lands outside the square?

  1. A)

    16\frac{1}{6}

  2. B)

    112\frac{1}{12}

  3. C)

    14\frac{1}{4}

  4. D)

    110\frac{1}{10}

  5. E)

    19\frac{1}{9}

Working