In this paper we explore the interrelationships of research in judgment and decision making with research in mathematical education on the learning of probability concepts. The psychological literature demonstrates that people are subject to heuristic and biases when making inferences or probabilistic estimates. The literature of mathematics education indicates that many people are statistically illiterate. Thus, central motivating questions for the paper are: Can research in the learning and teaching of probability and statistics help the statistically naive judge? Can research in the psychology of inference help the naive statistician? How can research from both these disciplines aid the teacher of probability and statistics? The paper consists of three main parts. Part one investigates obstacles to the use of statistics when making judgments or inferences. Part two discusses some suggestions from psychologists and from mathematics educators for increasing people's reliance upon statistics when making inferences. In part three, suggestions for further research are discussed. It is suggested that cooperative research efforts between psychologists and mathematics educators be conducted in order to further investigate these questions.