Question 19
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 chooses a distance uniformly at random from $[0, 1]$ and a direction uniformly at random from $\{\text{north}, \text{south}, \text{east}, \text{west}\}.$ All her choices are independent. She now hops the distance in the chosen direction. What is the probability that she lands outside the square?