In Exercises 19 and 20, suppose a mouse wanders through the given maze, some of whose doors are “one-way”: they are just large enough for the mouse to squeeze through in only one direction. The mouse still must move into a different room at each time step if possible. When faced with accessible openings into two or more rooms, the mouse chooses them with equal probability.

The mouse is placed in room 1 of the following maze.
a. Construct a transition matrix and an initial probability vector for the mouse’s travels.
b. What are the probabilities that the mouse will be in each of the rooms after 4 moves?

Transcribed Image Text:

1 2 + 4 5 3 6