**Abstract**

The mathematical probability concept was set forth by Andrey Nikolaevich Kolmogorov in 1933 by laying down a five-axioms system. This scheme can be improved to embody the set of imaginary numbers after adding three new axioms. Accordingly, any stochastic phenomenon can be performed in the set **C** of complex probabilities which is the summation of the set **R** of real probabilities and the set **M** of imaginary probabilities. Our objective now is to encompass complementary imaginary dimensions to the stochastic phenomenon taking place in the "real" laboratory in **R** and as a consequence to calculate in the sets **R**, **M**, and **C** all the corresponding probabilities. Hence, the probability is permanently equal to one in the entire set **C** = **R** þ **M** independently of all the probabilities of the input stochastic variable distribution in **R**, and subsequently, the output of the random phenomenon in **R** can be determined perfectly in **C**. This is due to the fact that the probability in **C** is calculated after the elimination and subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic phenomenon. 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:** degree of our knowledge, chaotic factor, complex random vector, probability norm, complex probability set **C**, momentum wavefunction, imaginary entropy, complex entropy
