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Power systems in industrialized countries are operated on the basis of an "N-1" or similar security criterion. This criterion guarantees that the system should be able to continue operating without involuntary customer interruptions in the event of the failure of any single component of the system. Incidents involving the near simultaneous failures of more than one component are deemed to have such a low probability that securing the system against their consequences is not considered worthwhile. Because catastrophic blackouts do happen in spite of the application of the N-1 criterion, one must conclude that quasi-simultaneous failures on multiple components do happen more frequently than one might think. Therefore, one should also consider whether this simple deterministic approach to power system security is still appropriate. This presentation discusses some of the issues associated with this cost/benefit approach.