Suppose that a student will be either on time or late for a particular class and that the events that he is on time or late for the class on successive days form a Markov chain with stationary transition probabilities. Suppose also that if he is late on a given day, then the probability that he will be on time the next day is 0.8. Furthermore, if he is on time on a given day, then the probability that he will be late the next day is 0.5.
a. If the student is late on a certain day, what is the probability that he will be on time on each of the next three days?
b. If the student is on time on a given day, what is the probability that he will be late on each of the next three days?