There are five cities where you are interested in taking a vacation. Instead of deciding where to spend your time, you choose to let probability decide for you. You start off in city A, which has trains going to each of the other four cities. You ride a train at random, which brings you to another city. You keep going in this manner until you decide enough is enough, and stay in the last city you end up in. Assume the train routes are as follows: City A has a train to all other cities City B has trains to cities A and C City C has trains to cities A and E City D has trains to cities A, B, and C City E has a train to city D You never stay in the same city until you are completely done riding trains. If you are equally likely to hop on any train leaving the city you are in, what is the probability of ending up in a particular city after a really, really big number of train trips (i. e. the steady-state probability)