### Formulate the transition matrix

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A copy machine is always in one of two states, either working or broken. If it is working, there is a 70% chance that it will be working tomorrow. If it is broken, there is a 50% chance it will still be broken tomorrow. Assume that one day is a natural time step.
(a) Draw a state diagram for the process and formulate the transition matrix
(b) Assuming the machine is working today, what is the probability that it will be working tomorrow? After one week? After one month?
(c) What is the long-term probability that the copy machine will be working on any given day?

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