I have 3 umbrellas. When I leave home or office, if it rains or if there are 3 umbrellas where I am, I will bring

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I have 3 umbrellas. When I leave home or office, if it rains or if there are 3 umbrellas where I am, I will bring an umbrella. The probability of raining when I leave home or office is 0.5. Find the transition matrix if the state variable is the number of umbrellas at home before I leave.

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