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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

Weather is modelled as a Markov chain on Sunny, Cloudy, Rainy. From Sunny the next day is Sunny, Cloudy, Rainy with probabilities 0.6,0.3,0.10.6, 0.3, 0.1; from Cloudy with probabilities 0.4,0.4,0.20.4, 0.4, 0.2; from Rainy with probabilities 0.25,0.25,0.50.25, 0.25, 0.5. Today is Sunny. What is the probability that the next three days are Cloudy, Rainy, Rainy in that order? Express your answer as a common fraction.