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This study has the purpose of addressing four questions that lie at the baseof the probability theory and statistics, and includes two main steps. Asfirst, we conduct the textual analysis of the most significant works written byeminent probability theorists. The textual analysis turns out to be a ratherinnovative method of study in this domain, and shows how the sampled writers,no matter he is a frequentist or a subjectivist, share a similar approach. Eachauthor argues on the multifold aspects of probability then he establishes themathematical theory on the basis of his intellectual conclusions. It may besaid that mathematics ranks second. Hilbert foresees an approach far differentfrom that used by the sampled authors. He proposes to axiomatize theprobability calculus notably to describe the probability concepts using purelymathematical criteria. In the second stage of the present research we addressthe four issues of the probability theory and statistics following therecommendations of Hilbert. Specifically, we use two theorems that prove howthe frequentist and the subjectivist models are not incompatible as manybelieve. Probability has distinct meanings under different hypotheses, and inturn classical statistics and Bayesian statistics are available for adoption indifferent circumstances. Subsequently, these results are commented upon,followed by our conclusions

Four Fundamental Questions in Probability Theory and Statistics