(Answered) A mouse after being placed in one of 4 rooms will search

Statistics

A mouse, after being placed in one of 4 rooms, will search for cheese in that room. If unsuccessful, after one minute it will exit to another room by selecting a door at random. (All the rooms connect to each other.) A mouse entering the room with the cheese will remain in that room. If the mouse begins in room 3, what is the probability that it will get trapped in the long run? Are there any absorbing states? I know that I have to set up a transition matrix, but I am having trouble after that. Can you help me?

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