ON CHOICE FROM FINITE VS INFINITE FIELDS IN COURSE OF PROBABILITY THEORY
1Krasnoshchekov V.V., 1Semenova N.V., 2Mohamed B.M.M., 3Bakkar M.M.A.
1 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia (195220, St. Petersburg, Polytechnicheskaya street, 29), e-mail: krasno_vv@spbstu.ru
2 Cairo University, Giza, Egypt (12613, 1 Gamaa Street, Giza, Egypt), e-mail: boss_3ds@yahoo.com
3 University Al-Baath, Damascus, Syria (PP75+5VC, Aleppo Highway, Damascus, Syria), e-mail: mamadyan1997@gmail.com
The authors continue to study the accuracy and limitations of applicability of probabilistic models. The concept of accuracy is an important component of the competencies of university graduates in the field of mathematical modeling. In this paper, the authors compare the probabilities calculated using exact and approximate formulas. The authors find the probabilities of selection from an infinite field of options using the exact Bernoulli formula, which, in this case, bases on the statistical definition of probability. Obviously, in practical problems, only a choice from a finite field of options is possible, then they make calculations according to the classical selection formula. The authors conduct all research on the material of the same task, which is neutral in terms of the content of the text, and, at the same time, allows for a simple interpretation of the results. The found values of the absolute and relative errors of calculating the probabilities demonstrate a fairly fast convergence of the approximate results to the exact ones. Thus, the authors empirically established the limit values of the size of the variants bank, at which the exact and approximate results differ by no more than 1%. The selected approximations of the lines of convergence give formulas for the minimum required size of the bank of variants. It is possible to use these formulas at medium risk levels of the processes under consideration.
Keywords: teaching the theory of probability, Bernoulli's formula, choice based on the classical definition, absolute error, relative error.