Mr. Smith reads local newspaper every day after which he puts it upon the top of pile on his desk. He tidies up his desk every afternoon. If there are more than 5 newspapers in pile then he puts the overall pile in the garbage, otherwise he does so with probability 1/3 (independently of his other decisions). Suggest the number of newspapers Xn in pile in the evening of day n, that is, after he tidied his desk.
(a) Can you model the procedure with Markov chain? If yes, determine the states and transition probabilities?
(b) Sunday evening the pile was empty. What is the probability that Thursday evening there is exactly one newspaper in the pile?