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 3 doors in the room. One door leads out
of the building after 3 hours of travel. The second and third
doors return to the room after 3.5 and 5.5 hours of
travel, respectively.
If the probabilities with which the group selects the three doors are 0.2,
0.2, and 0.6, respectively, what is the expected number of hours before
the group exits the building?