Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 05 (c)/Statement

Suppose four towns are connected by roads in the configuration shown below. A random driver wakes up every morning and flips a coin. If the coin is heads, she stays where she is for the day. If the coin is tails, she drives to the next town, choosing one of the roads with no preference. (For example, if she leaves Town A, she is equally likely to go to Town B or Town C, but she will not go to Town D that day.)

(c) What is the equilibrium probability of the system?