The decisive step for the theoretical foundation of statistical inference is associated with the development of probability calculations. The origin of this usually is attributed to questions posed to Pascal (1623-1662) by the famous knight Méré, for some authors an inveterate gambler, for others a philosopher and man of letters. However, it seems more likely to accept that the questions posed by Méré (1607-1684) were theoretical in nature and not the result of gambling. It also seems acceptable that it was not these questions that gave rise to the calculation of the probabilities. What is beyond doubt is that the correspondence between Pascal and Fermat (1601-1665) - in which both arrive at a correct solution to the famous problem of betting - represented a significant step forward in the realm of probability.

There are also authors who maintain that the calculation of probabilities originated in Italy with Paccioli (1445-1514), Cardano (1501-1576), Tartaglia (1499-1557), Galileo (1564-1642) and others. While it is true that Cardano in his book Liber de Ludo Aleae, in particular, did not go far from obtaining the probabilities of some events, the best way to characterize the group is to say that it marks the end of the prehistory of probability theory. Three years after Pascal predicted that the alliance of geometric rigor with the uncertainty of bad luck would give rise to a new science, Huyghens (1629-1645), enthusiastic about "giving rules to things that seem to escape human reason" published "De Ratiociniis in Ludo Aleae "which is considered to be the first book on calculating probabilities and has the remarkable particularity of introducing the concept of mathematical hope.

Leibniz (1646-1716), as an eclectic thinker he was, did not fail to deal with the odds. In fact, he published two works, one on "combinatorial art" and the other on the applications of probability calculations to financial matters. It was also due to Leibniz's advice that Jacques Bernoulli devoted himself to perfecting the theory of probability. His work "Ars Conjectandi" was published eight years after his death and in it the first limit theorem of probability theory is rigorously proved. It can be said that it was due to Bernoulli's contributions that the calculation of probabilities acquired the status of science. Fundamental to the development of probability calculations are the contributions of astronomers, Laplace, Gauss and Quetelet.

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