Amidwestern university has three types of health plans: a health maintenance organization (HMO), a preferred provider organization (PPO), and a traditional fee for service plan (FFS). In 2000, the percentages for the three plans were HMO: 30%, PPO: 25%, and FFS: 45%. Experience dictates that people change plans according to the following transition matrix:

(a) What will be the percentages for the three plans in 2001?

(b) What is the long-run fraction choosing each of the three plans?

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HMO PPO HMO 0.85 0.1 PPO 0.2 0.7 FFS 0.1 0.3 FFS 0.05 0.1 0.6