Crazy as it sounds, full scale nuclear war is not an extinction level event. Catastrophic, no doubt, and might reduce the human population by a couple orders of magnitude -- but unlikely to kill off all the humans. There just aren't that many bombs (~17,000 is a high estimate) and the earth is really really big. "Nuclear winter" appears to be overdramatized in fiction.
There's quite a lot of semiserious discussion of exactly this question on the internet; this is just a rough paraphrase of the consensus. It can make for a fun couple hours googling.
How many does it have to kill to be an extinction level event? By the time we deal with the radiation sickness and the lack of civilization would we have enough people left for a breeding population?
There's quite a lot of semiserious discussion of exactly this question on the internet; this is just a rough paraphrase of the consensus. It can make for a fun couple hours googling.