Each American family is classified as living in an urban, suburban or rural location. During a given year, 15% of all urban families move to a suburban location, and 5% move to a rural location; also, 6% of all suburban families move to an urban location, and 4% move to a rural location; finally, 4% of all rural families move to an urban location, and 6% move to a suburban location.   If a family now lives in an urban location, what is the probability that it will live in an urban area two years from now?    If a family now lives in an urban location, what is the probability that it will live in a suburban area two years from now?    If a family now lives in an urban location, what is the probability that it will live in a rural area two years from now?  Find the steady-state probabilities.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Each American family is classified as living in an urban, suburban or rural location. During a given year, 15% of all urban families move to a suburban location, and 5% move to a rural location; also, 6% of all suburban families move to an urban location, and 4% move to a rural location; finally, 4% of all rural families move to an urban location, and 6% move to a suburban location. 

 If a family now lives in an urban location, what is the probability that it will live in an urban area two years from now?  

 If a family now lives in an urban location, what is the probability that it will live in a suburban area two years from now?  

 If a family now lives in an urban location, what is the probability that it will live in a rural area two years from now? 

Find the steady-state probabilities. 

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