Do infants and preschoolers quantify probabilities based on proportions?

Most probability problems encountered throughout life require the ability to quantify probabilities based on proportions. Recent findings suggest that young children have this ability while other findings suggest otherwise. For example, when presented with transparent jars containing mixtures of preferred and less preferred items, 10- to 14-month-olds (Denison & Xu, 2014) but not 3- and 4-years-olds (Girotto, Fontanari, Gonzalez, Vallortigara & Blaye, 2016) seem to rely on the proportions of objects in the jars to predict the content of samples randomly drawn out of them. Other findings suggest that 12-month-olds do not rely on proportions of objects to make predictions, but rather that their intuitions are based on an evaluation of all possible outcomes a random process can generate (Téglás, Ibanez-Lillo, Costa & Bonatti, 2015). It is thus not clear whether the ability of infants have been overestimated in Denison & Xu (2014), whether the ability of preschoolers have been underestimated in Girotto et al. (2016), or whether the ability to rely on proportions to estimate probabilities follows a U-shaped curve during development. In our study, we tested again whether infants and preschoolers rely on proportions of objects to estimate probabilities of random sampling events. We presented children with two boxes containing a mixture of two types of objects – one type having a higher rewarding value. The experimenter sampled one object out of each box and hid them in two cups. Children could then choose between both cups. Our results show that neither infants nor preschoolers relied on the proportions of objects in the boxes to make inferences about the content of the cups and choose the sample with a higher rewarding value. However, it is not clear why infants failed, as they also failed in a condition in which the outcomes were certain. These findings are congruent with Girotto et al. (2016) but in contradiction with Denison & Xu (2014) and could indicate that infants' ability to reason about proportions have been over-estimated. However, more studies are necessary to explain why infants succeeded in Denison & Xu (2014) and failed in our task.