Lisa Crawford is getting into the moving-truck rental business in three nearby counties. She has the funds to buy about 100 trucks. Her studies show that 20% of the trucks rented in Bay County go to Sage County, and 15% go to Thyme County. The rest start and end in Bay County. From Sage County, 25% of rentals go to Bay and 55% stay in Sage, whereas the rest move to Thyme County. From Thyme County, 40% of rentals end in Bay and 30% in Sage.
a. Draw a transition diagram that displays this information.
b. Write a transition matrix that represents this scenario. List your rows and columns in the order Bay, Sage, Thyme.
c. What is the sum of the entries in row 1? Row 2? Row 3? Why does this sum make sense?
d. If Lisa starts with 45 trucks in Bay County, 30 trucks in Sage County, and 25 trucks in Thyme County, and all trucks are rented one Saturday, how many trucks will she expect to be in each county the next morning?