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2. Suppose Max lives in a 2-room apartment with his cat, who moves freely about the apartment. Over the last year, he has meticulously collected data on his cat's movements. Through painstaking statistical analysis, he has concluded that if the cat is in room 1, she has a 20% chance of being in room 2 an hour later; if the cat is in room 2, she has a 40% chance of being in room 1 an hour later. Today, Max left his apartment at 8AM. He didn't see where his cat was when he left, but from experience knew that there was a 25% chance that the cat was in room 1. a) Find the probability that the cat is in room 2 at noon. b) Find the steady state of this system