A drunken passenger has arrived at a small airport with a main area that leads to three gates (see Fig. 1). Going from the main area of the airport to gate 1 takes 5 minutes (one way), going to gate 2 takes 2 minutes (one way), and going to gate 3 takes 2 minutes (one way). Their flight leaves from gate 3 . If they walk to any of the other two gates, they will need to walk back to the main area of the airport. They are so drunk that whenever they are back in the main area, they choose each gate uniformly at random with probability 31. Figure 1: The airport map (a) What is the expected amount of time that will take the passenger to get to their gate? (10 pts) (b) If the passenger is at the airport main area and boarding ends in 12 minutes, what is the probability that they do not miss the flight? (10 pts)