Probability arises inherently from a lack of information. For example, if I were to take a ball out of a bag with 3 yellow and 2 white balls, I would have a 0.6 probability of getting a yellow and a 0.4 probability of getting a white ball. However, these only apply because I cannot see where each ball is located. However, if I had the information about the forces on each ball as they were thrown into the bag, as well as the angle of my arm as I put it in, I could, without doubt, know for sure which ball I would get.
Hence, is it not possible that the entire probabilistic nature of quantum mechanics arises entirely from our lack of information on phenomenon? I have read up on the Heisenberg uncertainty principle but it seems a bit iffy that physical phenomenon are purely bounded by mathematical theory. Could there be a non-probabilistic explanation for these phenomenon?