The goal the article is to answer the questions: "Why the probability theory and its applications should be studied?" and "What is the attitude of students to the study of probabilistic branches of mathematics?" The values of probabilistic branches of mathematics (stochastics) are revealed on the analysis of scientific publications on the philosophy and history of probability theory, as well as pedagogical works of mathematicians known for their achievements in this area. Further, to examine the attitude of students to study probability theory and its applications, a survey of 76 mathematics sophomores was conducted. The results of the survey were investigated using cluster analysis. It has been found that students, who have a positive attitude and motivation to study probabilistic branches of mathematics, realize the value of probabilistic ideas and methods at the philosophical level and recognize the practical utility of this. Therefore, the scientific publications on the philosophy and history of probability theory, as well as the pedagogical works of well-known mathematicians, can be the valuable resource that could be of use in the educational process to improve the motivation of students in learning probability theory.