On Conditional Probability Problem Solving Research – Structures and Contexts

In this paper we summarize our research on solving problems of conditional probability we have recently carried out. We investigate a particular world of school word problems we call ternary problems of conditional probability. We classify them into four families and twenty subfamilies depending on data structure and investigated students’ behaviour in solving problems, those with one conditional probability as known data. We identify four types of thinking processes related to data format and sense of use of data. With the help of a mathematical object, the trinomial graphs, and the analysis and synthesis method, we provide a didactical and phenomenological analysis of ternary problems of conditional probability in a particular context by identifying situations and contexts of use. Here we will illustrate our approach by the diagnostic test situation and the particular context of health. The main purpose of our work is to improve secondary school students’ understanding of conditional probability and their probability literacy by proposing a teaching approach based on problem solving in contexts.