Give a detailed explanation for this problem.

A mouse is placed in room #1 of the maze described in the gure below. A piece of cheese is placed in room #9. At each step the mouse chooses a room at random (uniformly among all accessible rooms) and moves into that room. (a) How many steps does it take on average until the mouse nds the piece of cheese ? (b) How many times does the mouse visit room #7 on average before reaching the cheese ? (c) We now add a cat in room #7. The cat doesn't move. What is the probability that the mouse finds the cheese before being caught by the cat ? 1 2 3 4 5 6 7 8 9 Note: This problem may require the use of R. If you decide to use R, please submit your code as part of your solutions. Bonus question: What if the cat is also allowed to move in the same way as the mouse