Programme générale

Chapitre 1 : Opérations sur les ensembles – Dénombrement – Analyse combinatoire

(Set Operations – Counting – Combinatorial Analysis / العمليات على المجموعات – العد – التحليل التوافقي)

Description (EN): This chapter introduces the basic concepts of ensemble and their operations (union, intersection, complement). It also presents the rules of dénombrement, such as permutations, arrangements and combinations, which are essential tools for calculating the possible cases in a probabilistic model

Chapitre 2 : Probabilité d’un événement

(Probability of an Event / احتمال وقوع حدث)

Description (EN): This part defines an expérience aléatoire, with événements élémentaires and compound events. It explores Kolmogorov’s axioms and the probability function, giving students the tools to compute the probabilité of both simple and complex événements

Chapitre 3 : Probabilité conditionnelle

(Conditional Probability / الاحتمال الشرطي)

Description (EN): This chapter focuses on the concept of probabilité conditionnelle. It studies independence between événements, the conditional probability formula, and Bayes’ theorem, which is widely used in fields such as reliability analysis and medical diagnosis.

—Chapitre 4 : Variables aléatoires

(Random Variables / المتغيرات العشوائية)

Description (EN): Here, students learn about variables aléatoires (discrete and continuous)

The chapter explains probability distributions, cumulative distribution functions, espérance mathématique, variance and higher moments. Classical laws such as binomial, Poisson, exponential and normal are introduced with practical examples