# Probabilistic Thinking from Elementary Grades to Graduate School

## Abstract

The study of probability began about 400 years ago with an attempt to address questions related to gambling. Although methods were quickly developed to work with certain types of problems, stating an actual definition of probability proved to be a long and difficult process, and even today there are differing opinions about how probabilities should be interpreted. This chapter introduces the subject through its historical roots and explores some of the ways in which people perceive probabilities. It then looks at how those perceptions have influenced the way probability is taught, all the way from kindergarten through graduate school. The chapter concludes with a brief look at the nature of interaction between mathematics and science.

## Keywords

Classical probability theory Frequentist probability theory Law of large numbers Measure theoretic probability probability Subjective probability theory## References

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