Question: A machine has three critical parts, numbered part 1, 2 and 3, which are subject to fail, but the machine can function as long as

A machine has three critical parts, numbered part 1, 2 and 3, which are subject to fail, but the machine can function as long as two of these parts are working. When two are broken, they are replaced at the end of the day and the machine is back to working order the next day. If we assume that parts 1, 2 and 3 fail with probabilities 0.01, 0.02 and 0.04, respectively, but no two parts fail on the same day. Please use a Markov chain to describe the model and find the corresponding transition probability matrix.

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