The paper Epistemological Frames of the Calculation of Probability focuses on the mathematical-philosophic problem of adopting the Theory of the Calculation of Probability. The theory passes through different “stages” and theory frameworks included in other scientific fields besides Philosophy, and encounters multiple inequalities. These inequalities will be discussed in the first part of this paper that is based on the epistemological explanation of the concept of the calculation of probability. Probability is in Philosophy seen through the empirical and a priori stance, all in the Theory of Foundationalism. An explanation was also contributed by Clarence Irving Lewis, who devoted a part in his work “An analysis of knowledge and valuation” to these inequalities in the Theory of Probability. That part of the paper will be titled Epistemological relation to the Calculation of Probability, and it will contain all essential elements of the epistemological understanding of the concept of probability. The second part of this paper will describe the mathematical explanation of that same concept, since this concept had to be developed parallel in this science as well in order to be better understood in theory. That part of the paper will cover terms such as Probability space, Random events, Successful outcome, Brown’s motion, but also other statistical terms that will be used in explaining the entire problem of the aforementioned theory and calculation. The statistical-mathematical segment of this paper is about in the same frame and scope as that of the main, epistemological. The second part is important for the understanding of the very concept of probability, and contains examples of cases that can be considered in both sides. The conclusion of this paper gives a concrete thought on the importance of the Calculation of Probability, especially in the epistemological framework