A mouse has to go through a maze (see gure below) to reach a piece of cheese. Whenever it reaches a dead end in the maze, it falls through a trapdoor and has to start at the beginning. Assume that the mouse does not remember any of the paths it took on its previous attempts. The mouse is twice as likely to go right than left, and twice as likely to go straight ahead than right, when all three choices are available. It is twice as likely to go straight than left or right, when only two choices are available. The mouse cannot go backwards. What is the expected number of attempts the mouse will make to go through the maze before it reaches the cheese