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
![](https://test.transtutors.com/qimg/9e98db62-f7c0-47a6-a172-df406f10749c.png)
What is the probability of generating a proper three-letter English dictionary word after two transitions from the initial state?