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The​ day-to-day changes in weather for a certain region form a regular Markov process. Each day...

The​ day-to-day changes in weather for a certain region form a regular Markov process. Each day is​ sunny, cloudy or rainy. If it is sunny one​ day, there is a 70% chance that it will be sunny the following​ day, a 20 % chance it will be​ cloudy, and a 10 % chance of rain. If it is cloudy one​ day, there is a 50 % chance that it will be sunny the following​ day, a 30 % chance it will be​ cloudy, and a 20 % chance of rain. If it rains one​ day, there is a 40 % chance that it will be sunny the following​ day, a 40 % chance it will be​ cloudy, and a 20 % chance of rain. In the long​ run, what is the daily likelihood of rain?

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