Do infants and preschoolers quantify probabilities based on proportions?

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.