Uncertainty plays a role in a variety of early learning processes such as numerical reasoning, language learning, and causal reasoning. Furthermore, adults experience probabilistic data in the course of numerous tasks every day. Thus, the ability to make accurate predictions about future events is a foundational skill which serves both child and adult. Researchers have studied the development of probabilistic reasoning for decades, providing data to suggest that , until early adolescence, children are incapable of accurately predicting future outcomes based on proportion. An equally long scholarly lineage has also provided evidence that adults rely on inaccurate heuristics and biases when reasoning about probability. If prediction is so vitally important to human judgment and decision making, why does the empirical literature suggest humans have impoverished decision making skills when reasoning about uncertainty? What mental representations do humans really on to calculate probability? How do these mental representations change with age and experience?

The current dissertation seeks to answer these questions by studying simple probability judgments made by children and adults. The empirical evidence provided here suggests that children and adults draw on analog magnitude representations of number in order to enumerate sets of outcomes. Furthermore, although both children and adults sometimes use inaccurate heuristics, children rely on these heuristics less with age and adults seem to use them when they perceive two outcomes to be equally likely. In chapter 2, I present findings from a series of experiments employing a non-symbolic ratio magnitude comparison task to investigate the relationship between number approximation, ratio processing, and probability estimation in adults. Empirical results reveal that performance on a probability discrimination task improves as the ratio of the two proportions increases and psychophysical modeling revealed that both numerical and non-numerical stimulus features such as field area, size, and sparsity influence probability estimation. Additionally, these findings reveal that probability estimation is influenced by formally incorrect heuristic decision rules or strategies. Furthermore, findings from two follow-up experiments indicate that these strategies are not influenced by the amount of time participants are given to compute probability and that they persist even when participants are informed that the use of this strategy is not always accurate. While previous research has investigated the influence of ratio processing and heuristic bias on probabilistic decision making, this series of experiments marks the first attempt to systematically investigate both the psychophysical properties of probability estimation and the factors which influence adults' use of heuristic decision rules in a non-symbolic probability discrimination task. Chapter 3 presents the findings from two experiments designed to investigate the developmental trajectory of children’s probability approximation abilities. These results indicate that probability judgments improve with age, become more accurate as the distance between two ratios increases, and that children’s perceived probability is influenced by the same psychophysical properties reported for adults (i.e. the size of the objects and the perceived numerosity of target objects). Older children’s performance suggested the correct use of proportions for estimating probability; but in some cases, children relied on heuristic shortcuts. Together, these results suggest that children’s non-symbolic probability judgments show a clear distance effect, and that the acuity of probability estimations increases with age. In chapter 4, I push this research further by investigating the influence of feedback on children’s use of heuristic decision rules. Results from two experiments reveal that children's use of heuristics can be overridden with the proper amount and type of feedback. Together, our findings indicate that children use heuristic decision rules to reason about the outcome of future events but that children can override the use of heuristics if they are provided with enough feedback on trials which conflict with their strategy. These results help shed light on the development of probabilistic reasoning and may lead to improved assessments of children's quantitative reasoning.

Together, the results reported in this dissertation suggest that human probabilistic reasoning is not as impoverished as previous research might suggest. Although children and adults sometimes use inaccurate heuristic decision rules to aid their decision-making, they are also capable of accurately calculating probability based on proportion. Furthermore, children can learn to reformulate their calculations of probability based on feedback and reach a more sophisticated understanding of the proportional nature of probability. These findings have broad implications for a variety of domains such as cognitive development, numerical reasoning, decision-making, strategy selection, and mathematics education.