The article discussesand analyz esmatters concernedwi the stimating the probabilities of significant but rare events, extreme and catastrophic situations in the electric power industry. Essentially, the problem is concernedwi thquantitatively estimating the extent of hazard (risk) and its acceptable levels. The complexity of making a nestimateiss temming from scarcity and uncertainty of relative unreliability of retrospective information, due to which it becomes impossible to obtainre liable, unbiased and consistent statistical estimates of the reliability, safety, and survivability indicators. The need of checking catastrophe occurrence conditions and probability when an electric power industry facility loses its serviceability due to having been affected by hazardous factors ispointedout. The mainattenti onispaid to methods for quantitatively estimating the technological risk and its indicators, and analysis examples are given. The statement soutlinedinthearti cleopen the prospects for further investigations aimed at estimating the probability of rare random events and catastrophes in the electric power industry, which is an extremely important problem.