Probabilidade Geométrica: dos problemas clássicos à modelagem de situações reais com uso do Geogebra e do Python.

Abstract

Geometric Probability is a branch of Probability Theory in which probabilities are determined through the ratio of geometric measures, such as lengths, areas, and volumes. Despite its potential to integrate concepts from Geometry, Probability, and Mathematical Modeling, this topic remains relatively unexplored in Basic Education. In this context, this dissertation aims to present a proposal for teaching Geometric Probability that combines mathematical foundations, classical problems, contextualized applications, and digital technologies. Initially, the main concepts of Combinatorics, Probability, and Plane Geometry necessary for the development of the topic are presented. Next, classical problems, such as the Spaghetti Problem, Bertrand’s Paradox, and Buffon’s Needle Problem, are discussed, highlighting different solution strategies and their geometric interpretations. Subsequently, original applications developed by the author using GeoGebra software and the Python programming language are presented, exploring situations related to soccer and demonstrating how these tools can contribute to the construction and analysis of mathematical models. As an educational product, a six-lesson teaching sequence is proposed, structured around investigative methodologies and the use of digital technologies. It is expected that this proposal will contribute to making the teaching of Geometric Probability more meaningful, contextualized, and engaging, while offering teachers an alternative approach to addressing this topic in Basic Education.