6. Consider a square with the vertices A, B, C, D, let S be the midpoint of that square. We start our journey from S. Then every round we can go to one of the points A, B, C, D, S according to the following rule: if we are in S', we can go to A, B, C, D with equal probability, if we are in one of the vertices A, B, C, D then we can go to one of the two adjacent vertices with probability 1/6 or to S with probability 2/3. . Find probability that we first reach A before we first reach B. . What is the probability that after 1000 rounds we stay at point S? . Find the expected number of rounds in which we first return to S