Mandelbrot's Discussion

Benoit and a student have agreed to meet to discuss probability. The student is punctual and will arrive at a uniformly random time between 4:00 PM and 5:00 PM. Benoit, however, will be a bit late and is expected to arrive at a uniformly random time between 4:30 PM and 5:00 PM. Each person is willing to wait for the other for up to 10 minutes. If the other person doesn't show up within this time frame, they will leave. What is the probability that their meeting successfully occurs?

Answer format: round to 3 decimal places.