A model for the evaluation of probabilities of rare events by combining the available experience with expert opinion is developed, using the core melt frequency of nuclear power reactors as an example. A distribution for this frequency is assessed using the statistical evidence and including “near misses.” This distribution is subsequently modified, via Bayes' theorem, to include the estimate derived by the Reactor Safety Study, which is treated as an expert's opinion. A probabilistic model for the credibility of this opinion that includes the critics' point of view is presented. The resulting (posterior) distribution is the assessed distribution of the frequency of reactor core melts based on a body of knowledge that includes the available experience and the WASH-1400 estimate.