Some questions of probability theory in a popular presentation

In this book, readers get acquainted with the evidence proposed by the author of the simplest version of the law of large numbers. 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 relationship between simple numbers and independence of events is indicated. It is shown how, using the correct coin, you can organize experience in which the probability of the onset of one of the outcomes of this experience is equal to anyone in advance a given number. It should be noted that almost all reasoning are based on the concept of equal -degree of events and the axiomatics of A.N. Kolmogorov is not used. Tasks are given for independent solution.
The book will be useful to students of the physical and mathematical classes of the school, as well as to all those who are interested in mathematics and probability theory