The Philosophy of Probability Values Behaviour through Fractions and Composite Probability Function for Independent Events in the Discrete Case

Abstract

This paper focuses on dealing with probability theory, and it adopted an objectivism philosophic approach, as well as a mathematical approach. These approaches aim to study the probability values behaviour as discrete quantities in the case of discrete sample space for independent events through fractions and composite functions. This requires a discussion of the usage of probability statements, the causes behind the existence of probabilistic phenomenon, and an explanation that admits to measuring causality in probability theory through the concept of complement and fractions. The paper uses an experiment with a design that addresses the shortcoming of traditional experiments through the concept of fractions. This, in turn, reflects some aspects of the probabilistic behaviour, including some important consequences that follow through. This paper also uses the relative frequency of events and the probability axioms, which provides the sample space to include all possible events in the form of sequences and sub sequences. The paper further provides some definitions that define some elements of the fractions probabilities and the sample space, alongside some proven propositions, lemma, and corollaries that admit to calculating composite probability functions. This is in addition to a brief discussion of the continuous cases.