jadrian,
You could have some insight by some readings about "random number generators" (rng).
You have very likely used -knowinggly or not- a random number generator.
An rng follows a perfectly deterministic process.
However, you might not know what this process (algorithm) is.
Furthermore, if you knew the algorithm you might still not be able to predict the result of the rng, simply because you may lack information about the initial value or the key that was used, or anything else.
In summary, you will quickly realize that randomness can often be related to a lack of information. This lack of information should not be seen as a failure of science. Nor should it be seen as a cheap story to hide difficulties. Recognizing properly the lack of information and its role in our analysis of the world is, on the contrary, I believe, a pillar of science.
I would even not be surprised that the whole quantum mechanics could also be approached in this way. It has already be hypothesed that the "wave function" is not a "real" physical object, but instead a mix of physical reality and of the information we have on this reality.
Only kids may learn more on this, for they have less prejudices.