Problem 3. A mouse maze consists of the paths shown below. At any intersection, the mouse is equally likely to select any of the available paths. 3 5 (a) Formulate the (one-step) transition matrix (b) Determine the probability that, starting at intersection 1, the mouse will reach inter- section 5 for the first time in 4 runs (1 run a run between two intersections)? (c) What is the expected number of runs needed for the mouse to reach intersection 5 from intersection 1 for the first time?