Passive safety systems are commonly considered to be more reliable than active systems. The lack of mechanical moving parts or other active components drastically reduces the probabilities of hardware failure. For passive systems, it is necessary to introduce the concept of functional failure, i.e., the possibility that the loads will exceed the capacity in a reliability physics framework. In this paper we analyze the passive cooling of a gas-cooled fast reactor, and we use an importance-sampling Monte Carlo technique to propagate the epistemic uncertainties and to calculate the probabilities of functional failures. The results show that functional failures are an important contributor to the overall failure probability of the system and, therefore, should be included in probabilistic risk assessments. A comparison with an alternative active design is considered also. The results show that the active system can have, for this particular application, better reliability than the passive one.