Let me try to give you a kitchen-table explanation.
I can't help you with statistics vis-a-vis quantum mechanics, but probability is very basic.
The underlying "real stuff" in quantum mechanics are numbers that, when squared, produce probabilities of seeing things.
Typically, these numbers are complex, but they don't always have to be.
These numbers are called amplitudes of the probabilities.
They are called that because, just as an electrical voltage is called its amplitude, and its energy is proportional to voltage squared, so in the quantum world probability is proportional to amplitude squared.
As I said, these amplitudes are treated as the underlying realities of everything.
They can be added to each other, because they are complex numbers.
For example, if you have two such numbers, each one can represent a probability, but when you add them together, the result could be larger than each one by itself, or it could be zero, if one number is the negative of the other.
So you see they can act like waves, either canceling or reinforcing each other.
If you think of tossing a die, with 6 numbered sides, the probability of each side (like 1) is 1/6.
The probability that you get either a 1 or a 4 (two particular sides) is 1/6 + 1/6 = 1/3.
However, in the quantum world, each side of the die has an amplitude, which is any complex number that when squared equals 1/6.
(Technically, you multiply it by its "complex conjugate".)
So, if you happen to have a die where the amplitude of 1 and the amplitude of 4 are opposites, the probability of (1 or 4) would be zero!
I still think the double-slit experiment is the best eye-opener for the relationship between probability and its amplitudes.