Students arrive at the professor's office for extra help according to a Poisson process with an average rate of 4 students per hour. The professor does not start the tutorial until at least 3 students are available. Students who arrive while the tutorial is going on will have to wait for the next session.
a. Given that a tutorial has just ended and there are no students currently waiting for the professor, what is the mean time until another tutorial can start?
b. Given that one student was waiting when the tutorial ended, what is the probability that the next tutorial does not start within the first 2 hours?