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The three letters C A and T represent the states

The three letters C, A, and T represent the states of a word- generating system. Let the initial state probability vector be (1/ 3 1/ 3 1/ 3) for the three letters, respectively. The transition matrix is given as

What is the probability of generating a proper three- letter English dictionary word after two transitions from the initial state?

What is the probability of generating a proper three- letter English dictionary word after two transitions from the initial state?

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