For some understanding of how the NRC conducts regulation of nuclear power plants...

A portion of their website is dedicated to risk assesment. Following major events such as those in Japan, Chernobyl, Three Mile Island and the Browns Ferry fire in 1975, risks are studied and re-evaluated to determine the need for changes in regulation. As an example, the fire in 1975 played a role in the development of Appendix R to 10 CFR 50. Other examples (some ongoing, others closed) of changes to regulations based on risk changes/identification can be seen in the Generic Issues section of the NRC site. Somewhat ironically, seismic issues affecting nuclear plants in the central and eastern United States have been on the scope for over five years (see GI-199 at http://www.nrc.gov/reading-rm/doc-collections/generic-issues/gis-in-implementation/). Given the nature of the topics being considered, this information includes some fairly significant discussions of probability (with the accompanying math).