The question is without realism. With six billion people on Earth it would be almost impossible to kill everyone. But far from that being a negative thing, mass destruction can be a boon for humanity. As Darwin showed, the evolution of a species is driven by the death of entire segments of the population. Those who survive are more suitable to the environment (In our case, "the environment" isn't just the ecosystem but also the social, political and technological environment we create around us).
Additionally, given our ability of self-change we've moved beyond genetic evolution and would more likely evolve by changing our ways rather than physically adapting (e.g. learning to not develop nuclear weapons rather than evolving a physical immunity to radiation). Hopefully we'd learn that the first time.
A little death and anarchy now and again is a good thing. In the grand scheme of things, it keeps the human animal on its toes.