A probabilistic system is one where events and occurrences cannot be predicted with precise accuracy. It is contrasted by a deterministic system in which all events can be predicted with certainty.
In a probabilistic system, unlike in a deterministic system, what has just occurred is not always an accurate predictor of what will transpire next. The weather, for example, is a probabilistic system, in that future events can only be imperfectly predicted.
The theory of probabilistic systems by extension leads to probabilistic analysis and forecasting. A probabilistic system must be analyzed according to the various possible outcomes and their relative probability of occurrence.