The article reports an empirical study on the introduction of elementary probabilistic concepts in school, focusing on tasks related to the psychological tradition of heuristics and biases. The concepts involved were studied using an extensional natural frequencies approach. We describe the school intervention conducted in an interaction across different school levels (5th and 9th grades) with the aim of promoting motivation and cooperation thereby strengthening learning. The different tests were assessed both qualitatively (based on argumentation analyses) and quantitatively. The results provide further evidence on the diversity of obstacles tied to probabilistic notions. More importantly, they exhibit an overall improvement in performance of students at both levels. This work confirms the efficacy of natural frequencies in eliciting the intended interpretation of probabilistic tasks and suggests that an appropriate interaction between different scholastic levels can be implemented as a fruitful learning arrangement.