Here is a simple random/deterministic hybrid:
0 with probability 35%
1 with probability 65%
Basically, any non-uniform probability distribution is "hybrid".
But such a system violates the definition [Aradia] gave before. If the system receives input before making a decision, that input is the cause of the processes that eventually lead to the decision. Then the "thought process" you talked about in your definition is not separate from past events.
Obviously, the internal structure of the system will also play a big role, but ultimately it was the input that led to a decision being made and also the nature of that decision. Basic stimulus-response relationship.
If you trace back the cause of the action, you'll find part of it in the input and the other part in the internal process. The outside world and the system are players that you must consider on equal footing: some phenomenon depend on the outside world alone, some phenomenon depend on both and some others depend uniquely on the system.
Imagine that the system wants to achieve goal X and devises a strategy that will achieve X on every single possible input. This can be trivial (return 3), or very complex (earn a million dollars). Arguably, the input conditions the reaction of the system, but ultimately, the result is that X will be achieved and you can't trace that particular result back to the input because it happens no matter what the input is. In other words, you can imagine non-trivial systems that react differently on different inputs yet always achieve a precise objective. Albeit, ultimately, the means of achieving it may be traced back to the input, the fact that the objective is achieved can only be traced back to the system.
To give you a semi-concrete example, imagine that you have to shoot a target. You have visual input and that input will tell you where to shoot. Nonetheless, when the target is hit, the ultimate cause isn't your visual input because had the target been elsewhere, you would have shot somewhere else, but the target would still have been destroyed. The result "target destroyed" does not depend on the input. You didn't choose where to shoot but you chose to shoot it.
Also note that you can swap the system and the outside world, in which case the "input" goes the other way around. Hence why I say they are on equal footing when you trace back the causes of phenomena
