In this paper, we will see the interest of the simulation of random experiments in a study of mathematics education, especially in probability modeling. Through simulations accompanied by a questionnaire, we were able to explore various conceptual difficulties among students concerning the teaching of probability theory at the university. Indeed, on the one hand, these difficulties revolve around the basic probabilistic notions,contributing to the modeling through the random variable notion. For example, difficulties to adopt the frequentist approach to estimate the fortune of the gambling player, difficulties in identifying a random experience, difficulties in constructing the random variable appropriate to a probabilistic situation, etc. On the other hand, this simulation innovation also allowed students to explore a cognitive model for two probabilities to have a “heads” and of intuitive estimation of ” the fortune of the player& quot; . Moreover, many students arrived to put the frequentist approach of probability on availability thanks to the observation of the repetitions whose simulation allowed them. The challenge of this work is to integrate numerical simulations int o teaching in order to explore the learning difficulties of students and to evaluate their learning. In this way, students will be able to construct their lively concepts, which will be available to engage in probabilistic modeling.

Keywords : Simulation, conceptual difficulties, random experiments, random variable, probabilistic modeling.