As a junior employee I get assigned a small office each year, with either 0, 1 or 2 office mates. The number of office mates I am assigned next year will be random, with each of 2 prospective office mates being given a certain independent probability of being assigned to me. If I have no office mates this year that probability of each person being assigned to me is .7: if I have one office mate this year, the probability of each person being assigned to me is .5; and if I have 2 office mates this year, the probability of each being assigned to me is .4. a) Write out the transition matrix for the probabilities of 0, 1, or 2 office mates next year, if I have 0, 1, or 2 office mates this year. b) If I have one office mate this year, what is the probability I will have 2 office mates the year after next