Probabilités 1

The Probability 1 module provides a fundamental introduction to the mathematical study of randomness and uncertainty. It is designed to equip students with essential tools for counting, analyzing, and modeling outcomes in various contexts such as science, engineering, economics, and data analysis. The module is organized into two major chapters: 

  • The first chapter, Combinatorial Analysis, focuses on methods for systematically counting the possible arrangements of a set of elements. It begins with the study of arrangements and permutations, both with and without repetition, before introducing combinations, which allow the selection of elements regardless of order. These techniques are crucial for solving problems where the total number of possible outcomes must be carefully determined. 
  • The second chapter, Calculation of Probabilities, presents the formal framework needed to describe random phenomena. It introduces the concept of a probabilistic space, the notion of events and their operations, and the structure known as an event tribe. The chapter then develops the definition and properties of probability, including the special case of equiprobable experiments and elementary events. Building on this foundation, it explores conditional probability, the compound probability formula, the total probability formula, and Bayes’ formula, all of which are essential tools for reasoning under uncertainty.