P =
[1/3, 2/3, 0, 0]
[0, 1/3, 2/3, 0]
[0, 0, 1/3, 2/3]
[0, 0, 0, 1]
A company has 2 machines. On any day, each machine that is working has a 1/3 chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility and will be working 2 days after it breaks down. Letting the state of the system be the number of machines working at the beginning of the day, formulate a transition probability matrix for this situation.
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