Abstract : This work is connected with random and, more exactly, with the introduction of probabilities in the middle school. It comes within the framework of the evolution of the syllabus which has officialized the “frequentist” approach of probabilities. We have dealt with what exists at the level of the pupils knowledge, in particular, the sort of notions previous to any school content (spontaneous knowledge) and also what can be done at the level of the introduction of probabilities at middle school. In order to study the spontaneous aspect of knowledge, we have used a series of diagnosis experiments made on some probability objects such as the notion of quantification of probabilities and the notion of the independence. The analysis tool adopted is the notion of conception, which is essential in our work, and emerges from the conceptual fields theory that we have formulated in terms borrowed from the Didactic Anthropological Theory. We have especially noticed the difficulty conceiving the independence of the events and the rarity of the appearance of the conception "favourable cases / possible cases". The need of an adequate teaching being shown, we have established a didactic experimentation in which we treat both "a priori" and "frequentist" approaches. In the analysis of this experimentation, we used, in particular, the articulation of the Theory of Didactical Situations and professional didactic. This analysis has provided us information with terms of prescribed tasks and effective ones, “milieu” and didactical contracts. In conclusion, the above mentioned experimentation represents an outline of a teaching sequence which should be collated with contingency.