Brochure written on the materials of the lecture delivered by the author on July 23, 2005 at the Summer School "Modern Mathematics" in Dubna . It is devoted to the formalization of such an intuitively clear term as “accident”. The brochure discusses four different approaches to this concept, based on the characteristic properties of random sequences: frequency stability, randomness, typicality and unpredictability. The concepts of enumerability, computability, entropy and Kolmogorov complexity, which are most important in the theory of algorithms, are introduced. With their help, we can try to answer the question that classical probability theory does not cope with: to determine whether, for example, an individual sequence of zeros and units can be considered random or not. The last chapter summarizes the concepts of frequency stability, randomness, typicality, and unpredictability in the case of computable distribution. Brochure addressed to senior schoolchildren and junior students. No preliminary knowledge will be required from the reader, but it will be useful to get acquainted with the theory of algorithms, and to read the last chapter - with the basic concepts of probability theory.