Question about quantum physics and possible shortcomings

I was originally an applied math major and about 2 years ago doubled up with a major in physics... Being an applied math major, I have had quite a few courses in mathematical modeling, and there was always something that bugged me about quantum physics. I figured that I would figure it out once I finally took a couple of courses in quantum, and even asked my professor, but this question has yet to be answered for me:

The Schrodinger equation is a mathematical model, or sometimes also referred to as a deterministic model... So why in the world are we associating a probabilistic function with it?

I'm not saying that it's wrong or that it doesn't provide insight, because it most definitely does and obviously has provided quite a revolution in modern technology. However, it does seem rather limiting to use a mathematical model in such a way...

Does anyone understand what I'm saying? Any insight would be greatly appreciated.
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Recognitions:
 Quote by galoisjr The Schrodinger equation is a mathematical model, or sometimes also referred to as a deterministic model... So why in the world are we associating a probabilistic function with it?
The Schrödinger equation determines a wave function w/o any uncertainty, probability, indeterminism or something like that. But what we are doing is to interpret this wave function as a probability density (of finding a single particle in a certain region).

Mentor
 Quote by galoisjr The Schrodinger equation is a mathematical model, or sometimes also referred to as a deterministic model... So why in the world are we associating a probabilistic function with it?
Because experimental outcomes are probabilistic, in general, as far as we know.

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