Why does intuition deceive? Chance explained by mathematics

Abstract

Chance is a central element in decision-making under uncertainty. This paper discusses the importance of randomness in developing probabilistic reasoning, exploring how human intuition often fails when dealing with seemingly simple situations influenced by hidden or partial information. Using three problems—the Monty Hall Problem, a medical case involving diagnostic tests, and an airport scanner case—we address fundamental concepts such as conditional probability and Bayes’ Theorem. Through simulations and mathematical formalizations, we demonstrate how correctly updating probabilities in light of new evidence can impact decisions in areas like medicine, statistics, and even games. The paper also highlights the pedagogical role of these problems in mathematics education and critical thinking development.