Most statistical problems encountered throughout life require the ability to quantify probabilities based on proportions. Recent findings on the early ontogeny of this ability have been mixed: For example, when presented with jars containing preferred and less preferred items, 12-month-olds, but not 3- and 4-years-olds, seem to rely on the proportions of objects in the jars to predict the content of samples randomly drawn out of them. Given these contrasting findings, it remains unclear what the probabilistic reasoning abilities of young children are and how they develop. In our study, we addressed this question and tested, with identical methods across age groups and similar methods to previous studies, whether 12-months-olds and 3- and 4-years-olds rely on proportions of objects to estimate probabilities of random sampling events. Results revealed that neither infants nor preschoolers do. While preschoolers’ performance is in line with previous findings, infants’ performance is difficult to interpret given their failure in a control condition in which the outcomes happened with certainty rather than a graded probability. More systematics studies are needed to explain why infants succeeded in a previous study but failed in our study.

Children were recruited from a database of families who had voluntarily registered and agreed to participate. They were from mixed socioeconomic backgrounds and some family were plurilingual.

Each child underwent a preference test, a probability condition and a baseline condition. In the preference test, the experimenter presented children with two different Kinder eggs capsules, one empty and white and the other containing a fingerpuppet and blue. She hid both objects in separate cups and let subjects choose a cup (only subject choosing the cup containing the blue egg were kept in the final sample). In the probability condition, the experimenter presented subjects with two populations of Kinder eggs, one containing a higher proportion of blue eggs and the other a higher proportion of white eggs. She secretly drew one object out of each population, hid them in separet cups and let subjects choose between both cups. The same procedure was repeated in the baseline condition, in which one population only contained blue eggs and the other only white eggs. 

Every session was video recorded. Children's choices were coded from the videos. We coded it as a success when children chose the sample drawn out of the population with a higher proportion of blue eggs and as a failure when they chose the other sample.