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A copy machine is always in one of the two states, either working or broken. When it is working, there is a 70% chance which it will be working tomorrow. When it is broken, there’s a 50% chance it will still be broken tomorrow. Suppose that one day is natural time step.

a) Sketch a state diagram for process and formulate the transition matrix

b) Supposing the machine is working today, what is the probability that it will be working tomorrow? After one week? After one month?

c) What is long-term probability that the copy machine will be working on any prearranged day?

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