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.
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