Mathematical aspects of digital technologies: The problem of the absent-minded passenger

The example of the absent-minded passenger problem illustrates the fundamental difficulty of estimating practical values of probabilistic parameters on the basis of general theorizing and allows us to give more accurate and subtle estimates of various parameters, as well as their practical computable approximation. This article is important for building systems of artificial intelligence and artificial consciousness, as well as for modern didactics of higher education, especially for the disciplines of “applied mathematics” and “theoretical computer science”. It is shown that a detailed study of a random process provides more significant applied materials than formally correct theoretical calculations.