Some issues of probability theory in the popular presentation (region). Vinogradov O.P.

In this book, readers get acquainted with the evidence of the simplest version of the law of large numbers proposed by the author. The tasks that make it possible to prove a series of identity that are used in the theory of ally -willed (Egyptian) fractions and Fibonacci numbers are considered. The classic task of ruin when playing two players in the gambling game is considered. Examples are given from which it follows that the intuitive concept of the independence of events cannot answer the question whether events are independent in the “mathematical” sense. The connection between simple numbers and independence of events is indicated. It is shown as using the correct coin to organize experience in which the probability of the onset of one of the outcomes of this experience is equal to anyone in advance the given number. It should be noted that almost all reasoning is based on the concept of equal ministry of events and the axiomatics of A.N. Kolmogorov are not used. Tasks for independent solution are given.

The book will be useful for students of the physical and mathematical classes of the school, as well as to all those who are interested in mathematics and probabilities theory.