Question 5 (6 marks, C5) A miner Eric is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him to safety after 9 hours of travel. The second door leads to a tunnel that will return him to the mine after 7 hours of travel. The third door leads to a tunnel that will return him to the mine after 5 hours. Let X denote the amount of time (in hours) until Eric reaches safety, and let Y denote the door that Eric initially chooses. Assume that Eric is at all times equally likely to choose any one of the doors. (a) Explain why E(X|Y = 3) = E(X) + 5. [2] (b) What is the expected length of time until Eric reaches safety? [4]