This is an interesting probability problem. There are multiple variations of this. I am presenting a simple version.

There are three persons A, B and C who are aiming to settle a dispute the old dueling style except there are three of them. Here are the rules..

a. At random, it is decided what will be the sequence in which they will fire
b. When a person’s chance comes, that person is given at random the target (one of the other two) to shoot at
c. A is a sure shot (100% chance he will shoot the person dead), B is less so – has 80% chance of succeeding and C is a neophyte – 50-50 chance that he will succeed with a shot.
d. They keep on with this sequence of shooting till one man is left.
e. There are no other extraneous conditions – e.g. no stray bullets etc etc.
f. What are the probabilities of A, B and C surviving?