Your dreams and probability theory

This article analyses from a statistical and probabilistic point of view the mechanism and interpretation of games of chance involving the removal of balls from an urn. To do thats, the concepts of random variable, sample space, expectation and expected value are introduced. To illustrate these concepts, a simple example is developed, in which the expected value of the game is compared to the cost of taking part in it. Then, these theoretical concepts are applied to a real example: the Christmas Lottery. By analyzing statistically the various prizes and their associated probability, the article concludes that the expected value of the prize is approximately two thirds of the invested money. This means that, in the long term, for every euro invested only 0.66 € are recovered. A simulation carried out with these data graphically proves this result, showing also the fact that dividing the total expenditure into several numbers increases the likelihood of increasing the number of prizes won, although the asymptotic value is still two-thirds.