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

From UBC Wiki

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

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.