A bus arrives at a bus stop at a randomly selected time

Question

A bus arrives at a bus stop at a randomly selected time within a 1-hour period. A passenger arrives at the bus stop at a randomly selected time within the same hour. The passenger will wait for the bus up to one-quarter of an hour. What is the probability that the passenger will catch the bus? [Hint: Let X₁ denote the bus arrival time and X₂ the passenger arrival time. If these arrivals are independent, then