The development of probabilistic reasoning during early childhood

Previous results have been inconsistent regarding the age at which children can compute probabilities based on proportions, with estimates ranging from one to 12 years. The aim of our study was twofold: (I) to address previous inconsistencies and (II) to quantify reasoning skills in 3- to 5-year-old children using an experimental procedure that is simple and engaging but also allows for the control of possible competing heuristic strategies, which may lead to outcomes mimicking the correct answer. Specifically, children had to choose between two urns containing varying proportions of blue and yellow balls. They knew they would receive a reward if, after several random mixtures, a target (e.g., a blue) ball fell out of the chosen urn. If children understood probabilities, they should select the urn with a higher proportion of target balls. Alternative reasoning strategies were disentangled by manipulating the absolute and relative numbers of target versus non-target balls in the two urns across 18 trials. We found that most 5-year-olds and a smaller but non-negligible number of younger children consistently chose the urn with a higher proportion of target items. However, a significant portion of 3- and 4-year-olds' responses appeared to be guided by heuristic strategies, with the most prevalent being choosing the urn with a higher number of target balls. These results provide a more comprehensive understanding of the development of probabilistic reasoning in young children and underscore the importance of using experimental procedures and stimuli that enhance reasoning abilities while controlling for competing strategies.