This paper is inspired by the recent work of Theofanous et al on the risk of liner failure in Mark-I containments. In that work, the authors presented a probabilistic framework and methodology for dealing with uncertainties surrounding “Level 2,” i.e., post-core-melt phenomena in nuclear plants. In so doing, they have advanced the state of the art of risk assessment and decision making in regard to such phenomena. The key ideas in this framework and methodology have application, of course, beyond Level 2 phenomena. The purposes of the present paper are to abstract and lift out these key ideas so that they can be seen more clearly and to place them in context along with similar ideas used elsewhere, particularly in seismic risk assessment and in the treatment of through-wall cracking and pressurized thermal shock transients. The author hopes, in this way, to clear up confusion and to advance the cause of consistency in the use of the words “probability,” “uncertainty,” “frequency,” “variability,” “randomness,” etc.