Probabilidade geométrica com abordagem na esperança Matemática - Jesus, Marco Antônio de (Universidade Federal do Tocantins, 2018)
The initial studies of combinatorial analysis and probability have a strong relationship with gambling, we recall a game with data practiced by Antoine Gombaud (Chavalier de Méré). He says that after a successful strategy (throwing a die four times and get a 6), achieving significant gains, he modified the game to two dice and would win if there were a double 6 in 24 throws, and in this accumulates loss. Detail marking his astounding with Blaise Pascal. This stimulates the study of probability in discrete spaces. The discrete probabilistic concepts (finite enumerable set) used by Pascal in solving the Méré problem are not sufficient to respond to problems of a continuous nature. For example, the problem of French needles Georges Louis Leclerc (count of Buffon) and other situations involving the calculation of probability in segments of straight lines, areas of flat figures or volumes of solids, as well as in a game applied during a fair of mathematics for primary school students (6th to 9th grade) of elementary education II. Using the “TURNEDWON” game it is possible to explore the concept of geometric probability, compare the result of the application with the calculations made and approach the mathematical hope when the game is performed a significant amount of times. Hope is an expectation of “ middle ” gain, a convergence, around an “ expected ” result. In this we will make a characterization of geometric probability and mathematical hope, finally we will apply these concepts in the resolution of problems of a continuous (geometric) nature.