2023 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 19 Hard

Sonya the frog chooses a point uniformly at random lying within the square [0, 6] \times  [0,6] in the coordinate plane and hops to that point. She then randomly chooses a distance uniformly at random from (0, 1] and a direction uniformly at random from north, south east, west. All he choices are independent. She now hops the distance in the chosen direction. What is the probability that she lands outside the square? (2023 AMC10B Q19)

  • A.

    \frac { 1 } { 6 }

  • B.

    \frac { 1 } { 1 2 }

  • C.

    \frac { 1 } { 4 }

  • D.

    \frac { 1 } { 1 0 }

  • E.

    \frac { 1 } { 9 }

Answer:B