Markov Chains & Long-Run Behavior · Medium problem

Each year, people move between City, Suburbs and Rural areas. Of those in the City, $80\%$ stay, $15\%$ move to the Suburbs and $5\%$ move to Rural areas. Of those in the Suburbs, $10\%$ move to the City, $80\%$ stay and $10\%$ move to Rural areas. Of those in Rural areas, $10\%$ move to the City, $10\%$ move to the Suburbs and $80\%$ stay. In the long run, what fraction of the population lives in the Suburbs? Express your answer as a common fraction.