The continued and extended use of nuclear power is often considered and discussed as a viable energy policy option to meet energy demands while also meeting national CO₂ emission reduction goals. A central issue in energy policy for sustainability is the question of nuclear reactor safety. However, studies on nuclear reactor safety often run up against the problem of estimating the probability of a major accident from patchy and limited empirical data. Here, we describe a simple probabilistic model of catastrophic nuclear reactor accidents based on a set of four assumptions. The model treats the accident probability in each of n reactors as a variable and returns the probability of a major accident in the reactor fleet. We find that, at 99.5% reactor safety, the probability of another Chernobyl- or Fukushima-sized event is 49% for the global fleet, and that safety would have to be 99.96% in order to bring that probability below 5%. We discuss our findings in light of the debate on energy policy for sustainability.