This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
You enter a town that has K killers and P pacifists. When a
pacifist meets a pacifist, nothing happens. When a pacifist meets a
killer, the pacifist is killed. When two killers meet, both die.
Assume meetings always occur between exactly two persons and the pairs
involved are completely random. What are your odds of survival?
Regardless of whether you are a pacifist or a killer, you may disregard
all events in which a pacifist other than yourself is involved and
consider only events in which you are killed or a pair of killers other
than yourself is killed.
Thus we may assume that there are N killers and yourself. If N is odd,
your odds of surviving are zero. If N is even, it doesn't matter to
you whether you are a killer or not. So WLOG assume you are. Then your
probability of survival is 1/(N+1).