Question

Alice and Bob visit the gym on Saturday for their hourlong workouts. Alice always arrives between 2:00 and 3:00 and Bob between 2:30 and 3:30. Assuming their arrival times are drawn independently and uniformly from the specified intervals (i.e. any arrival time in the given window is equally likely), and assuming they each stay for precisely one hour, what is the probability that on any given Saturday there exists a moment in time when all two are present at the gym? Please express your answer as a fraction in lowest terms.

Answer 1