You find out yourself trapped underground in mines, and you come to a room which contains 3 doors. One door leads to the tunnel that will lead you out of mine after 6 hours of walking another door leads to the tunnel which will lead you out after nine hours of walking the 3rd door leads to the path that winds circuitously through the mine and unfortunately will take you back to the exact same room after 12 hours of walking
Because of darkness and exhaustion, each and every time you return to this room you will have completely forgotten what door you may have selected previously. Thus suppose that each time you visit this room, you always choose one of the doors comletely at random, independentlly of any previous choices. With this assumption, determine the expected time that you will spend in the mine?