Noções de probabilidade e aplicações ao caso discreto

Abstract

The objective of this study is to o er the students and teachers of graduation courses that own a reduced workload, like Business, Accounting, Psychology, Information Systems and others, a text which facilitates the intuitive understanding of the Theory of Probabilities. The text addresses the three existent de nitions of probability with several examples of application and states some properties with a few demonstrations. It begins with the notion of wining or losing a game, known as the Theory of Chance. This intuitive notion became science starting the de nition of probability given by Laplace, known as equiprobabilistic model, which reduces all the facts of the same gender to certain number of cases equally possible. The interest is to calculate the chances of occurrence of an event from the de nition given by the reason between the number of favorable cases to the experiment (event) and the number of possible cases (sampling space). Then to show the limitation of this model, which is on counting the elements of sampling space. In the cases which the use of counting techniques are not enough, it is used the fequencial model that consists in repeating, in similar conditions, one experience n times and verify if the event A occurred in nA of these experiences. The probability of A event is thus de ned as being the limit of reason nA/n when n ! 1. But it is not always possible to repeat one experience in the same conditions. Hence there is the subjective de nition, in which is up to the interested use his/her knowledgement \a priori" making it possible to calculate the probability of an event occurs, probability \a posteriori". However as this subjective de nition considers the evaluation of the observer's belief in the occurrence of one experiment, it should stipulate some guidelines to be followed. With the objective of establishing some general rules and of rational behaviors, Kolmogorov created a de nition of probability based on three axioms. From this de nition it was possible to create varied probabilistic models with some well de ned hypothesis. As several real situations approach to these hypothesis, these models are very useful in the study, with the purpose of solving problems that involve several discrete or continuous random variables. Thus the importance of functions and distribution of discrete probabilities with some examples of application.