When talking about probability and determinism, we should also notice that there is an important difference between "deterministic" and "predictable." "Deterministic" is a property of a mathematical model, not a property of a universe. You look at the model, and you discover if it is deterministic or not, there's no mystery there. "Predictable", on the other hand, is a real-world application, something you cannot just tell you have to test it. So the usual rules of testing come into play-- you have measurement errors, and confidence intervals, all things you don't have to worry about to tell if a model is deterministic or not.
So for example, if you use a particular set of equations, like Lorenz did, to model weather, then you can just look at those equations and see they are deterministic. Formally, all that is required is that exact input data maps one-to-one to exact output data, and it's a deterministic model. But it's not quite that simple, because to use the meaning "data", we have to make contact with actual numbers we can manipulate, and they are not exact. But it's not a problem, we can still recognize a deterministic model if if has the straightforward property that a neighborhood of an input datapoint maps into a neighborhood of an output datapoint, and if you make the output neighborhood arbitrarily small, there is an input neighborhood that accomplishes that, even if you cannot actually compute that input neighborhood for practical reasons. If we can mathematically prove that our model has that property, it makes no difference if we are able to actually compute that one-to-one connection or not-- the model still has the attribute of being "deterministic."
So weather equations are generally deterministic, even if they are chaotic. But they are not predictable, because in practice you often cannot actually compute that mapping between neighborhoods, so you cannot compute the image of an input neighborhood such that it falls entirely within some narrowly selected target output neighborhood, because of the way errors magnify. That means that no matter how good your initial measurements are, you cannot successfully predict the distant future, as with weather-- but that's chaos, not indeterminism. Chaotic models are usually fully deterministic, and impossible to predict. So when models with those attributes are used to describe the universe, we find the intersection between deterministic and probabilistic behavior. The model is deterministic, the application of the model is probabilistic, and the universe is just the universe.
We already know that thermodynamics and statistical mechanics are like this, and some hold that quantum mechanics is too-- it is a chaotic application of some underlying deterministic model (say, Bohmian). But it's still not the universe that can have that property, it is a property of the models we use to describe the universe. All we can test about the universe is whether or not we can predict it, and so far with most things, we cannot.
