two questions about Markov chain?

#1 Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state.

Empirical data show that if the particle is in State 1, then it is 5 times more likely to go to State 2 at the next step than to State 3. If it is in State 2, then it is 6 times more likely to go to State 3 at the next step than to State 1. If it is in State 3 then it is equally likely to go to State 1 or State 2 at the next step.

Let A be transition matrix for this markov chain. Find a31, a32, and a33 (i.e., find the last row in the transition matrix)


#2 In any given year a person may or may not get the flu. Past records show that if a person has the flu one year then (due to a build up of antibodies) there is a 85% chance that they will not get the flu in the following year. If they don't have a flu in a given year then there is a 25% chance that they will get the flu the following year.



(a) If a person does not have the flu one year, what is the probability that they will also not have the flu 2 years later?

(b) In the long run, what proportion of years does a person not have the flu?