**3.3 A concise interpretation of the original** *CPP* **paradigm**

To summarize the novel *CPP* paradigm, we state that in the real probability universe **R** the degree of our certain knowledge is undesirably imperfect, and hence, unsatisfactory, thus we extend our analysis to the set of complex numbers **C**, which incorporates the contributions of both the set of real probabilities, which is **R** and the complementary set of imaginary probabilities, which is **M**. Afterward, this will yield an absolute and perfect degree of our knowledge in the probability universe **C** ¼ **R** þ**M** because *Pc =* 1 constantly and permanently. As a matter of fact, the work in the universe **C** of complex probabilities gives way to a sure forecast of any stochastic experiment, since in **C** we remove and subtract from the computed degree of our knowledge the measured chaotic factor. This will generate in universe **C** a probability equal to 1 (*Pc*<sup>2</sup> <sup>¼</sup> *DOK* � *Chf* <sup>¼</sup> *DOK* <sup>þ</sup> *MChf* <sup>¼</sup> <sup>1</sup> <sup>¼</sup> *Pc*). Many applications which take into consideration numerous continuous and discrete probability distributions in my 19 previous research papers confirm this hypothesis and innovative paradigm [4–22]. The Extended Kolmogorov Axioms (*EKA* for short) or the Complex Probability Paradigm (*CPP* for short) can be shown and summarized in the next illustration (**Figure 2**):
