Science:Math Exam Resources/Courses/MATH152/April 2022/Question B2 (a)/Solution 1

According to the hint, the transition matrix has $ij$-entry equal to the probability of going from state $j$ to state $i$ (where states A, B, C are thought of as labelled by the indices 1, 2, 3, respectively):

$$\left[{\begin{array}{ccc}0.7&0.2&0.2\\0.2&0.6&0.4\\0.1&0.2&0.4\end{array}}\right].$$

Note that the transpose of the transition matrix is different, although it contains the same information, and would not work in exactly the same way in the follow-up questions.