If half the population were murderers, and they could only kill once, how many would survive?

Question

So here's the rules: - Half the population are murderers - Each murderer can only kill once - We assume the nobody will fight back, and only murderers can murder - Murderers can kill other murderers - Only one murder can be committed at a time, no simultaneous murders - No suicide - This means there will be at least one surviving murderer - Everybody, including murderers, has an equal chance of being killed - It should be obvious, but murderers cannot kill if they've already been killed - Nobody is dying of old age or giving birth - it's an infertile and immortal (but not invincible) society - Murders occur every second, or whatever measure of time suits your taste - Murders are instant How many people should statistically survive? What proportion of them would be murderers? How would you go about working this out?

Answer 1

May we take the naive approach and assume uniform distribution?

If so, then half of the murderers and half of the innocents shall be killed.

So there will be 50% of the original population : 25% murders and 25% innocent.