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The pattern of sunny and rainy days on the planet Rainbow is a homogeneous Markov chain with two states. Every sunny day is followed by another sunny day with probability 0.8. Every rainy day is followed by another rainy day with probability 0.6.
a) Today is sunny on Rainbow. What is the chance of rain the day after tomorrow?b) Compute the probability that April 1 next year is rainy on Rainbow.
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