[tsimionescu]

I don't understand what you mean. NP is not N multiplied by P, it is the name of a set, the set of all problems which can be solved by a Nondeterministic algorithm with Polynomial time complexity. P is the name of the set of all problems which can be solved by a deterministic algorithm with Polynomial time complexity. The P=NP problem is a set identity problem, it's not an algebraic equation.

Note that here nondeterministic algorithm can be thought of as an algorithm which can try every value in parallel when faced with any choice, even an infinite amount of values. For example, a nondeterministic algorithm can try every number in R in parallel. There is no known way to replace this nondeterminism with probabilistic methods.