Danny,
Good point about thermodynamics.
In the evolution process it may be possible to calculate some things also, but the problem here is that the influences, then number of external parameters in the formulas are to large.
True, but the complexity of the model does not mean that it's "pure mathematical randomness". Similarily, current weather models are believed to be relatively deterministic in principle (that's why our supercomputers allow us to predict weather patterns for the next day or two), but in practice the complexity of those patterns is so mind-boggling that we like to simply the description of such phenomena by calling them "random".
As I said thousands of different probability distributions have been observed in nature. Let's not put them all in the same bag.
Pole