Consider a mouse (or rabbit, or other dumb aninal of your choice) that is inside a room (or cell) with THREE doors. The doors behave as follows:
- The first door leads to a tunnel that will take the mouse back to the room after two days
- The second door leads to a tunnel that will take it back to the room after four days
- The third door will lead the mouse to freedom after one day
- Every time the mouse is in the room, it chooses one door randomly, with equal probability.
- The time the mouse spends choosing a door can be disconsidered
- The mouse is dumb enough to choose the same door more than one time. i.e., it can theoretically stay in the room forever if it never chooses the right door.
Given this situation, we ask, how long does it probably take until the mouse REACHES freedom?