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Populations shifts in a certain city follow a particular pattern every year. If a person is living in the city they will stay in the city 0%0% of the time, move to the suburbs 50%50% of the time, and move out-of-state 50%50% of the time. If a person is living in the suburbs, they will move into the city 20%20% of the time, stay in the suburbs 30%30% of the time, and move out-of-state 50%50% of the time. If the person lives out-of-state, they will move to the city 10%10% of the time, move to the suburbs 80%80% of the time, and stay out-of state 10%10% of the time. In the long-run, what is the probability that a person will live out-of-state?
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