The brochure was written based on a lecture given by the author on July 23, 2005 at the “Modern Mathematics” summer school 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 most important concepts in the theory of algorithms are enumerability, computability, entropy and Kolmogorov complexity. With their help, you can try to answer a question that the classical theory of probability cannot cope with: to determine whether, for example, an individual sequence of zeros and ones can be considered random or not. The last chapter summarizes the concepts of frequency stability, chaoticity, typicality and unpredictability in the case of a computable distribution. The brochure is addressed to high school and junior students. No prior knowledge is required from the reader, but familiarity with the theory of algorithms and, for reading the last chapter, with the basic concepts of probability theory will be useful.