Nowadays, probability calculus is an instrument used for understanding our reality. It deals with examining the rules of accidental events, i.e. the events the course of which we are not able to foresee. They are called random events. Examining them, we usually consiously focus only at some of their causes and we analyse the frequency of the events with the same set of causes. Probability is a theoretical equivalent to a frequency notion.

Pierre Laplace based the notion of probability on the theory of combinations, defining probability as a quotient of the number of ways in which a certain event can occur and a total number of all possible situations. However, the assumption that all the elementary events in question are equally probable is a serious limitation here. Although Laplace definition allows to calculate the probability in many cases, it cannot be used when the number of possibilities is infinite or when the analysed situations are not equally probable.

A wide use of probability calculus in economics, military issues and science has made it necessary to systematize and state precisely its fundamental notions. It was achieved by Kolmogorov (in 1933) who  give the axioms of probability calculus. We will use his definition of probability in this lecture.

This lecture is the first one of the three dedicated to the elements of discrete probability. We will present the terms of a random event and operations made using random events as well as the notion of probability and its basic properties. We are aware of the fact that the majority of readers won't find this subject new to themselves: there are many secondary schools that offer a good level of probability courses. However, as we find the subject very important for the future computer scientists we thought it necessary to present or remind its basic elements.