**Abstract**

The system of axioms for probability theory laid in 1933 by Andrey Nikolaevich Kolmogorov can be extended to encompass the imaginary set of numbers and this by adding to his original five axioms an additional three axioms. Therefore, we create the complex probability set **C**, which is the sum of the real set **R** with its corresponding real probability, and the imaginary set **M** with its corresponding imaginary probability. Hence, all stochastic experiments are performed now in the complex set **C** instead of the real set **R**. The objective is then to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the "real" laboratory. Consequently, the corresponding probability in the whole set **C** is always equal to one and the outcome of the random experiments that follow any probability distribution in **R** is now predicted totally in **C**. Subsequently, it follows that chance and luck in **R** is replaced by total determinism in **C**. Consequently, by subtracting the chaotic factor from the degree of our knowledge of the stochastic system, we evaluate the probability of any random phenomenon in **C**. My innovative complex probability paradigm (*CPP*) will be applied to the established theory of quantum mechanics in order to express it completely deterministically in the universe **C** ¼ **R** þ**M**.

**Keywords:** chaotic factor, degree of our knowledge, complex random vector, probability norm, complex probability set **C**, position wave function

*"Nothing in nature is by chance … Something appears to be chance only because of our lack of knowledge."*

*Baruch Spinoza. "You believe in the God who plays dice, and I in complete law and order." Albert Einstein, Letter to Max Born "Without mathematics, we cannot penetrate deeply into philosophy. Without philosophy, we cannot penetrate deeply into mathematics. Without both, we cannot penetrate deeply into anything … "*.

*Gottfried Wilhelm von Leibniz.*

*"There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy."*

*Hamlet (1601), William Shakespeare*
