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The failure–repair (FR) model is one of the standard examples of a Markov chain

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The failure–repair (FR) model is one of the standard examples of a Markov chain. It is as follows. Suppose an office has a computer for its daily routine work. The administrator staff turns on the computer as she comes to work each day. Turning on the computer is referred to as a trial. The computer fails to turn on (work) with probability q. The probability that it turns on and functions normally is p, p q + = 1. Each time the computer fails to work, a repairperson (an IT personnel) is called. The computer cannot be used until it is completely repaired. We want to find the probability that the computer is in working condition at a specific number of trials.