Consider a production system composed of two machines, where only one machine needs to be operational at any given time. The breakdown probability of any operational machine on any given day is 0.2....

Consider a production system composed of two machines, where only one machine needs to be operational at any given time. The breakdown probability of any operational machine on any given day is 0.2. In case of a machine failure, the production is stopped for the day, and is resumed the next day with the other machine (if available). The repair job of the failed machine also starts the next day. It takes two days to repair a machine, and both machines can be repaired simultaneously.
1) Define the state space and draw the state transition diagram.
2) Starting with two available machines at the beginning of the first day, what is the probability that both machines are unavailable at the end of the 3rd day?
3) In the long run, what is the ratio of the days that both machines are unavailable?