Locked in a dungeon, you are faced with five doors. One of them leads to freedom. The other four will lead you back to the starting room disoriented and confused, so that you will not remember which of the doors you have already tried and have to start again.
How many attempts do you expect to make on the average (statistically) before making it out?
Going through a door, there is an 80% change you will be back in the same situation you were in previously (i.e. not escaped).
So, if N is the average number of doors you will go through to escape, then:
N = 1 + 0.8 * N
0.2 * N = 1
N = 5
Simpler Solution
