Two machines are available to perform a task: primary and back-up. Only one machine can be used on a given day and only one machine can be repaired on a given day. The primary is used whenever possible and is also always repaired first. If a working machine is available at the beginning of a day, it will be used to perform a task. Each time the primary machine is used during a day. it may malfunction with probability 0.02. If backup is used, it will malfunction with probability0.3. A repair on a malfunctioning machine will be attempted on the next day, and it succeeds with probability 0.86 for the primary and 0.80 for the backup. Model the system as a Markov chain, so that you can then keep track of whether the task can be performed on a given day or not. Draw the transition diagram and the transition matrix.

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