Question 5) (20 points) A rat is trapped in a maze. Initially, it has to choose one of two directions. If it goes to the right, then it will wander around in the maze for three minutes and will then return to its initial position. If it goes to the left, then with probability 1/3 it will depart the maze after two minutes of travelling, and with probability 2/3 it will return to its initial position after five minutes of travelling. (a) (10 points) Assuming that the rat is at all times equally likely to go to the left or the right, what is the expected number of minutes that it will be trapped in the maze? (b) (10 points) Suppose now instead that the left direction leads to the maze exit after two minutes of travelling and more importantly suppose that the rat learns (i.e., the rat does not choose the direction that led it earlier back to the initial position). What is the expected number of minutes that it will be trapped in the maze? Question 6) (10 points) If two fair dice are rolled, what is the probability that the sum of the two numbers that appear will be greater than 4