From Risk Analysis of Nuclear Deterrence by Martin Hellman. See also http://nuclearrisk.org/
A full-scale nuclear war is not the only threat to humanity’s continued existence, and we should allocate resources commensurate with the various risks. A large asteroid colliding with the Earth could destroy humanity in the same way it is believed the dinosaurs disappeared 65 million years ago. Such NEO (near earth object) extinction events have a failure rate on the order of 10-8 per year [Chapman & Morrison 1994].
During one century, that failure rate corresponds to one chance in a million of humanity being destroyed. While 10-6 is a small probability, the associated cost is so high—infinite from our perspective—that some might argue that a century is too long a delay before working to reduce the threat. Fortunately, significant threat reduction has recently occurred. Over the last 20 years, NASA’s Spaceguard effort is believed to have found all such potentially hazardous large asteroids, and none is predicted to strike Earth within the next century. With a hundred-year safety window in place, resolution of later potential impacts can be deferred for a few decades until our technology is significantly enhanced. Comets also pose a threat, and their more eccentric orbits make them harder to catalog, but their lower frequency of Earth impact makes the associated risk acceptable for a limited period of time.
While much less accurate than the in-depth studies proposed herein, it is instructive to estimate the failure rate of deterrence due to just one failure mechanism, a Cuban Missile Type Crisis (CMTC). Because it neglects other trigger mechanisms such as command-and-control malfunctions and nuclear terrorism, this appendix underestimates the threat. This simplified analysis uses the time-invariant model described in footnote 3. It also assumes that the experience of the first 50 years of deterrence can be extended into the future.
Since conditional probabilities were used, they can be multiplied, yielding an estimated range of (2•10-4, 5•10-3) for [...] the failure rate of deterrence based on just this one failure mechanism. The upper limit 5•10-3 is within a factor of two of my estimate that the failure rate of deterrence from all sources is on the order of one percent per year, and even the lower limit is well above the level that any engineering design review would find acceptable.