Nornagest comments on Welcome to Less Wrong! (July 2012) - Less Wrong
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The last survey reported that Less Wrongers on average believe that humanity has about a 68% chance of surviving the century without a disaster killing >90% of the species. (Median 80%, though, which might be a better measure of the community feeling than the mean in this case.) That's a lower bar than actual extinction, but also a shorter timescale, so I expect the answer to your question would be in the same ballpark.