One of the basic principles of risk management is that we should always keep an eye on ways that things could go badly wrong, even if they seem unlikely. The more disastrous a potential failure, the more improbable it needs to be, before we can safely ignore it. This principle may seem obvious, but it is easily overlooked in public discourse about risk, even by well-qualified commentators who should certainly know better. The present piece is prompted by neglect of the principle in recent discussions about the potential existential risks of artificial intelligence. The failing is not peculiar to this case, but recent debates in this area provide some particularly stark examples of how easily the principle can be overlooked.