The Philosophy of Probability Values Behaviour, through Fractions and Composite Probability Function in the Continuous Case

Abstract

This paper deals with probability theory, and it is an extension to a published paper that has the same title, but for the discrete case. This present paper is aiming to study probability values behavior, in the case of continuous sample space, through fractions intervals and composite function. This aim tends to study the value behavior rather than finding the value itself. Also, this aim requires usage of some concepts of continuity, geometric probability, and measure theory, which also need a brief treatment. This paper is mainly using an experiment with a design that helps to study the probability fractions values in the form of intervals in the case of one direction movement and in the case of different directions. As a result, every case reflects some aspects of probability values behavior and can clarify many important characteristics of the probability theory. In addition to applying the composite function by some important theorems of conditional probability. These are besides a proven proposition that helps to design experiment, upon the understanding of the case nature. In addition to a corollary that allows to visualize negative probability values, as a particular case (trial), that upon the validity of the explanation of negativity which should be consistent with the probability axioms.