The work experience of the coal mines in the methane-bearing deposits, numerous cases of accidents and injuries due to explosions of methane-air and methane-dust-air mixtures, quantitative indicators of the death of miners in the twentieth century and partly in the twenty-first century are given in the article. It is shown that at the methane-bearing coal deposits during the underground works the nature prepared the likelihood of accidents, the death of miners and the economic losses. This is due to the natural factors, organizational and social causes, violations of the provisions of the regulatory acts and instructions, technological and industrial discipline. The probability is adopted as the indicator of emergency situations on gas and dust, which is estimated by the product of the probabilities of gasifying the mine atmosphere and ignition of explosive mixtures. The risks of the formation of explosive mixtures at highly hazardous production facilities of various industries have the specifity. This is primarily the need to increase the activity of the supervisory authorities in meeting the requirements of instructions in the field of industrial safety, compliance with safe working conditions. Risk criteria and their classification are considered depending on the frequency of hazardous events and the number of injured, the quality of expert organization conclusions on the commissioning of hazardous facilities in various conditions and planned tasks. The issues are topical, which are related to prediction of hazardous phenomena, substantiation of technical and technological solutions for their prevention based on the positive work experience of the objects and new science proposals for justification of the parameters for their implementation at the enterprises for which it is basic to have hazardous working conditions and the risks of explosive situations.