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Folk wisdom holds that in the summer it rains 1/3 of the time, and that a rainy day is followed by a second one with

Folk wisdom holds that in the summer it rains 1/3 of the time, and that a rainy day is followed by a second one with probability 1/2. Supposing that the weather can be modeled by a two-state Markov chain, what is its transition matrix?

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