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

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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 1 (122.49 KiB) Viewed 23 times

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 1/4 or to S with probability 1/2. • 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.