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At all times, a bowl contains three pieces of fruit, which are either apples or oranges. Each hour, someone walks into the room and chooses

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At all times, a bowl contains three pieces of fruit, which are either apples or oranges. Each hour, someone walks into the room and chooses a piece of fruit at random. 60% of the time, they will replace it with an apple, and 40% of the time they will replace it with an orange. Let the state of the system at any hour (Xt) be the number of apples in the bowl. Find the onestep transition probability matrix for this Markov chain. Be sure to label the matrix appropriately

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