There are three categories of people Indonesia: those who never avoid to excercise,

those who sometimes do it, and those who always do it. Based on research shows that:

For those who did not avoid to exercise last year, 97% continue in the same category this year, 2% move to the "sometimes" category, and the remainder move to the "always" category.

For those who sometimes avoid to excercise, 5% move to "never," 90% stay the same, and 5% move to "always."

for the "always" avoiders, the respective percentages are 0%, 4%, and 96%.

Question :

a) Express the problem as a Markov chain. In the long run, what would be the steadystate probability of "never," "sometimes," and "always" tax categories? For those who did not avoid to exercise,

b) what is the probability of become an "always" avoider in 6 years ?

note : please dont forget question b