Chapter 9.1, Problem 93E

Health plans. A midwestern university offers its employees three choices for health care: a clinic-based health maintenance organization (HMO), a preferred provider organization (PPO). and a traditional fee-for-service program (FFS). Each year, the university designates an open enrollment period during which employees may change from one health plan to another. Prior to the last open enrollment period, $20\%$ of employees were enrolled in the HMO, $25\%$ in the PPO, and the remainder in the FFS. During the open enrollment period, $15\%$ of employees in the HMO switched to the PPO and $5\%$ switched to the FFS, $20\%$ of the employees in the PPO switched to the HMO and $10\%$ to the FFS, and $25\%$ of the employees in the FFS switched to the HMO and $30\%$ switched to the PPO.

(A) Write the transition matrix.

(B) What percentage of employees were enrolled in each health plan after the last open enrollment period?

(C) If this trend continues, what percentage of employees will be enrolled in each plan after the next open enrollment period?