In a large metropolitan area, commuters either drive alone (A), carpool (C), or take public transportation (T). A study showed that 80% of those who drive alone will continue to do so next year, while 15%will switch to carpooling and 5% will use public transportation. 90% of those who carpool will continue, while 5% will drive alone and 5% will use public transportation. 85% of those who use public transportation will continue, while 10%will carpool and 5%will drive alone. Write the transition probability for the model. In the long run what fraction of commuters will use the three types of transportation?