[ketozhang]

Yes you're right, every superposition of quantum systems have a real valued probability distribution for some observable variable.

QM has very specific rules when it comes to how two random variables are dependent. That specific rule comes up when you have quantum interference and this is best described by the conjugate square of two complex functions A^2 + B^2 + A*B + B*A. This is just a special case of the union probability: P(A) + P(B) - P(AB).