Lesson 1

Problem. A sports broadcaster wishes to predict how many Michigan residents prefer University of Michigan teams (known more succinctly as “Michigan”) and how many prefer Michigan State teams. She noticed that, year after year, most people stick with their preferred team; however, about 3 percent of Michigan fans switch to Michigan State, and about 5 percent of Michigan State fans switch to Michigan. However, there is no noticeable difference in preferences across the state's population of \(10\) million; in other words, it seems Michigan sports fans have reached a stationary distribution. Find the fraction of Michigan fans. (Example credit: Brilliant.)