In quantum mechanics, an electron doesn't have a definite position or momentum. It has a wave function from which the probability of finding it at a particular position or momentum can be calculated. An electron bound to a proton will probably be very near the proton.
Is an electron's path inherently non-deterministic -- i.e., is it unlike billiards in that if you know the starting velocity and mass of one ball you can calculate the rest of its path entirely. Or is it that, it is just impossible for observers to figure out this data, and thus we have to rely on probability calculations?
If it is not simply a case of being unable for us to observe, then I will be very confused. Does that mean "randomness" exists? That would seem extremely... illogical? But obviously I'm missing some pieces of understanding.