Using Simulations to Enhance Understanding in Probability

Reading the papers in the 2022 Special Issue of the CJSMTE dedicated to the teaching and learning of probability, we realized that we could contribute further to the topic by showing how coding (computational thinking), in particular computer simulations, can be used to enhance intuition and understanding of important probabilistic concepts and ideas. The focus of this article is not on coding, nor on learning how to code. Instead, through discussing five examples, we illustrate that coding can be a powerful tool, able to provide deep insights into concepts in probability that otherwise might not be as easy to reach. Written in Python, the simulation codes are short and can be used as an invitation to students to explore and play, and to further experiment with the probabilistic ideas that we discuss. The first two examples address the conceptualization of probability and the relation between the mean of a sample and the mean of the population. The remaining three examples, inspired by questions coming from real-life situations, cover reasoning about rare events, the study of population dynamics in an ecosystem, and testing for a medical condition.