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 ; from Cloudy with probabilities ; from Rainy with probabilities . 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.