We propose a statistical approach to achieving the task of calculating the probability of exceeding threshold concentration of an atmospheric admixture. Calculations were made for the case study on the spread of nitrogen dioxide emitted from two power plants in Novosibirsk. The fields of admixture concentration and its variance, as well as the probability of exceeding threshold concentration of an atmospheric admixture at a given point are calculated for different times of a day and wind speeds. In a series of calculations, it was shown that the probability of interest here depends in a complex way on thermal atmospheric stratification and on the concentration field of an atmospheric admixture. In particular, during a summer day the dependence of the probability on threshold concentration looks like a steep "step". Quite the opposite situation is observed at night, when curves of the probability versus admixture concentration are substantially flattened. This is because the probability density function of an atmospheric admixture concentration has a bimodal shape.