The original extended model of eight axioms (EKA) of A. N. Kolmogorov was connected and applied to numerical analysis and to chaos theory. Thus, a tight link between the novel paradigm and the theory of chaos was realized. Therefore, the “Complex Probability” model was more elaborated beyond the scope of my 36 previous published works on this topic.

Additionally, it will be demonstrated and shown in the new paradigm and in the following chapters, that before the beginning of the probabilistic phenomenon and at its end we have the degree of our knowledge (DOK) is 1 and the chaotic factor (Chf and MChf) is 0 since the random effects and fluctuations have either not begun yet or they have finished and completed their job on the random system respectively. During the nondeterministic experiment and system execution we have also: –0.5 ≤ Chf < 0, 0 < MChf ≤ 0.5, and 0.5 ≤ DOK < 1. We can notice that we have continuously and constantly during the entire process. This can be explained by the fact that the event that behaved stochastically and randomly in the set R is now deterministic and certain in the set of probabilities C = R + M, and this is after eliminating and subtracting the chaotic factor from the degree of our knowledge and hence after adding to the random phenomenon executed in R the contributions of the set M. Moreover, the imaginary, real, complex, and deterministic probabilities acting on any object have been computed in the three probabilities sets which are M, R, and C by , , Pc and Z respectively. Therefore, the novel CPP parameters DOK, Chf, MChf, Pc, Pr, Pm, and Z are perfectly and certainly guessed and foretold in the set C of complex probabilities with Pc kept equal to one enduringly and repetitively.

**Author(s) Details:**

** Abdo Abou Jaoudé, **

Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.