Summary: ISyE 3232 Exam # 2
Please be neat and show all your work so that I can give you partial credit.
(30) 1. Consider a drunkard who is walking on a circle. He can only stand
on one of five positions, equally spaced on the circle, labelled, 1, 2, 3, 4, and
5. At any step, the probability that he makes one step in the counterclockwise
direction is 0.6 and step in the clockwise direction is 0.4. Find the long-run
probability that he will be in position 5.
(30) 2. Cars at a washing facility have to go through a washing station and
then a drying station. These stations can only serve one car at a time. If an
arriving car finds the washing station busy, it has to wait. After being washed,
it can move to the drying station immediately if that station is free; if not,