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Probability space As in every game of chance, we are interested in making predictions for the events regarding the outcomes of lottery, the draws. In lottery, there are no opponents or a dealer in the game, so the only events to deal with are the outcomes of the machine that performs the drawing. These events can be described as the occurrences of certain numbers or groups of numbers (combinations) having a specific property (for example, those containing certain given numbers or numbers with a specific property). Every drawing is an experiment generating an outcome: a combination of n different numbers from the m numbers in play (see the denotations of the parameters in the previous chapter). The set of these possible combinations is the sample space attached to this experiment. The sample space is the set of all elementary events (i.e., events than cannot be broken down into units of other non-empty events). Normally, an elementary event would be any number combination that could occur as the result of drawing. Thus, an elementary event is any number combination (x1, x2 ,, xn ) that is possible to be drawn. This choice is convenient because it allows us to make the following idealization: the occurrences of all elementary events are equally possible. In our case, the occurrence of any number combination is equally possible (if we assume a random drawing and nonfraudulent conditions). Without this equally possible idealization, the construction of a probability model within which to work is not possible. We have established the elementary events and the sample space attached to a drawing as being the set of all possible elementary events (let us denote it by Ω ). This set has Cmn elements (all combinations of m numbers taken n at a time) and these numbers are generally very large, so the elements of the set cannot realistically be enumerated. Moreover, this enumeration would not have any practical purpose from mathematical point of view. 16PDF Image | THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems
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