In a popular tale of wizards and witches, a group of them finds themselves in a room with doors which change position, making it impossible to determine which door is which when the room is entered or reentered. Suppose that there are 4 doors in the room. One door leads out of the building after 4 hours of travel. The second and third doors return to the room after 4 and 4 hours of travel, respectively. The fourth door leads to a dead end, the end of which is a 2 hour trip from the door. If the probabilities with which the group selects the four doors are 0.2, 0.1, 0.2, and 0.5, respectively, what is the expected number of hours before the group exits the building