1. The problem statement, all variables and given/known data A taxicab moves between the airport, Hotel A, and Hotel B according to a Markov chain with transition probabilities: P(airport → A) = 0.7, P(airport → B) = 0.3, P(A → airport) = 0.9, P(A → B) = 0.1, P(B → airport) = 0.8, P(B → A) = 0.2. A-If the taxicab starts at the airport, what is the probability that it will be at Hotel A two moves later? B-Suppose the taxicab starts at the airport with probability 0.6 and starts at Hotel A and Hotel B with probability 0.2 each. What is the probability that it will be at Hotel B two moves later? C- In the long run, what fraction of visits will the taxicab make to each of the three locations? 2. Relevant equations 3. The attempt at a solution I have gotten the answer for parts A & C but I don't understand at all how I would set up the matrix with part B. My initial though was that the matrix was 0 .2 .8 .2 0 .8 .6 .4 0 with the first row/column being hotel A, the second row/column being hotel B, and the third row/column being the airport then by squaring the matrix I got .52 .32 .16 .48 .36 .16 .08 .12 .8 and then to get B I added up .32 + .12=.44 which was wrong. What did I do wrong?