An Uber driver moves between the airport A and two hotels B and 0 according to the fol- lowing rules. If the driver is at the airport, they will be at hotel B next with probability 1/4 and at hotel C with probability 3/4. If at a hotel, they will return to the airport with probability 4/ 5 and go to the other hotel with probability 1 / 5. Assign each state the following values: A=0, B=1, 0:2. (a) Find the transition probability matrix for this Markov chain. (b) Suppose the driver is initially at the airport. Find the probability for each of their three possible locations after 3 trips. (c) Suppose the driver is initially in hotel B. After 3 trips, in which location do we expect the Uber driver to be at? (d) Find the stationary distribution of the chain by solving an apprOpriate system of equa tions. Interpret your nal result in the context of the