Answer Happy

Problem 1: Consider the maze shown below. There are three cells (Cell 1, Cell 2, and Cell 3) and two permanent outcomes (Cheese heaven, and chased by a cat). A mouse is initially placed in Cell 1. When the mouse enters cell i, he wanders around within the cell for Xi minutes, where X, is uniformly distributed between 0 and 3i minutes, and then exits the cell by picking one of the doors at random (eg. if there are three doors, the mouse picks each with probability 1/3). Find the probability the mouse gets the cheese. NNN 1 2 3 • Problem 2: Find the probability that the mouse visits cell 3 before ending the maze (before getting to one of the two permanent outcomes). • Problem 3: What is the expected number of doors the mouse goes through before ending the maze? Problem 4: What is the expected number of minutes that the mouse stays in the maze?