(solution) A certain town never has two sunny days in a row. Each day is classified as rainy, cloudy, or…

(solution) A certain town never has two sunny days in a row. Each day is classified as rainy, cloudy, or…

A certain town never has two sunny days in a row. Each day is classified as rainy, cloudy, or sunny. If it is sunny one day then it is equally likely to be cloudy or rainy the next. If it is cloudy or rainy then it remains the same 1/2 of the time, but if it changes it will go to either of the other possibilities with probability 1/4 each. In the long run what proportion of days in this town are sunny? Cloudy? Rainy?