III. Expectation problem:

A student gets lost in Northern New York state in the mid night, on her way driving back to her apartment in NYC. Suppose she does not have access to the map or GPS, and she finds that in front of her, there are three routes for her to choose from. The first route (assume its Rt. 1) will bring her back to the same starting position after two and a half hours, due to detour and road construction. The second route (assume its Rt. 2) will complicate her sense of direction and bring her back to the same starting position, after driving for three hours. The third route (assume its Rt. 3) will lead her successfully to NYC, after three hours. Suppose at all the time, the probabilities for her to choose from those three routes are kept the same (memorylessness, so the probability to choose the first route is the same even after she chooses that route and returns to the starting point), what is the expected time (in hours) that she will arrive in NYC.