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?
c) if i find i am stuck in this position for my entire career, what is the probability in a given year of having 0 office mates? of having 1 office mate? of having 2 office mates?