Keyword: «probability theory»

The modern digital transformation of the educational environment makes it necessary to update approaches to teaching mathematical disciplines, in particular probability theory and mathematical statistics. Despite the fundamental importance of the course, it is often perceived by students as abstract one and inapplicable in practice, which reduces learning motivation and hinders the development of applied mathematical and digital skills. The aim of the article is to substantiate and develop methodological approaches for integrating practice-oriented tasks using artificial intelligence (AI) and programming tools (primarily Python) into the course of probability theory and statistics at the university. This will enhance the connection of theory with practical tasks and develop digital and research competences. Research methods: analysis of domestic and foreign literature, study of state and international documents, and pedagogical experiment. Modern approaches to learning were used as the basis: activity-based, competence-based and constructivist approaches, as well as the principles of digital didactics. The empirical part is implemented through the development and testing of practical tasks in the Python environment using the example of a course for second-year students of Vologda State University. The main results demonstrate that the integration of programming and AI tools enhances students' motivation, improves the quality of learning, reduces the time required to solve practical problems, and improves the nature of learning activities. The pedagogical experiment showed a 10% increase in the number of correct answers on the final test and a 15-minute reduction in the time required to complete practical tasks, along with increased student engagement. The theoretical significance lies in the description of a new model of teaching statistics, which combines approaches from pedagogy, mathematics and modern information technology. Practical significance lies in the development of applicable methodological recommendations and tasks that can be implemented in the educational process of universities and adapted for instruction of related mathematical disciplines using AI and programming.