Show that in both Example and the example just given the probability of absorpti

Show that in both Example and the example just given the
probability of absorption in a state having genes of a particular type is equal
to the proportion of genes of that type in the starting state. Show that this
can be explained by the fact that a game in which your fortune is the number of
genes of a particular type in the state of the Markov chain is a fair game.5 18
Assume that a student going to a certain four-year medical school in northern New
England has each year a probability q of ?unking out a probability r of
having to repeat the year and a probability p of moving on to the next year
(in the fourth year moving on means graduating).(a) Form a transition matrix for this process taking as
states F 1 2 3 4 and G where F stands for ?unking out and G for
graduating and the other states represent the year of study.(b) For the case q = .1 r = .2 and p = .7 find the time a
beginning student can expect to be in the second year. How long should this
student expect to be in medical school?(c) Find the probability that this beginning student will
graduate.