Teaching Complex Probability Problems Using Simple Simulations with Applications to the Broken Stick Problem

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By substantially reducing the stress caused by complex mathematical calculations, simulations help students focus on the key concepts of complex probability problems. Furthermore, the programming languages, such as R and Python, can be easily implemented in classrooms to perform simulations that allow students and teachers to discuss the idea to solve the probability problems step by step. This article presents a classical probability problem known as 'the broken stick problem' to show the efficiency of the simulations in teaching probability. It contrasts the effectiveness of mathematical and computational simulation approaches to the solutions of the broken stick problems with several variations. For concrete illustrations, a series of R codes and their examples are provided at the end of the article, which can be used for the simulation study in probability class with various versions of broken stick problems. The extension of the computational approach to other historic probability problems is also discussed. [For the complete proceedings, see ED626149.]