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How often is the server overloaded?

A web server is either healthy or overloaded each minute, and the next minute depends only on the current one:

  • If healthy now, it becomes overloaded next minute with probability 0.10.1 (and stays healthy with probability 0.90.9).
  • If overloaded now, it becomes healthy next minute with probability 0.40.4 (and stays overloaded with probability 0.60.6).

In the long run, what fraction of minutes is the server overloaded?

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