Risks to human beings arise from an inherent characteristic to make plans and try to make them happen, while external forces resist and tend to move our endeavours away from the plan. Any such "endeavour" is a complex ensemble of a bewildering variety of interacting elements which together form something "whole", usually called a "system" (e.g. a chemical process plant, a nuclear power plant, the stock market, air traffic control). A system has a certain state in the present and subsequent states in the future. There are deterministic and probabilistic systems and corresponding approaches to analyse them, that is to make their current states apparent and predict their future behaviour. In this paper, it is shown in which ways both analyses appear in risk analysis and it is hypothesised that both approaches are modelling the same process, though probabilistic analysis may reveal more information since it explicitly incorporates uncertainty in the form of numbers (and "there is safety in numbers"). The overall objective of this paper is to make clear what the differences between the two approaches really are. Their respective main strengths and weaknesses are discussed. A more refined objective is to discuss the specific role of probabilities in risk analysis. Examples of both approaches are given from applications in the nuclear power and chemical process industries, and some of the main problems encountered thereby are identified. Further, the challenge to system analysis posed by "chaos theory" is discussed. Due to its non-linear dynamic character, the future behaviour of a "chaotic system" is difficult to predict over a long period of time because it depends on arbitrarily small and thus not observable variations in the current state. Such behaviour might have serious consequences for human operators involved in the control of such systems. The paper concludes that, although both approaches to risk analysis can provide adequate safety levels to systems if applied in a correct and non-biased way, probabilistic methods seem to be more cost-effective and the results easier to communicate to decision-and policy-makers.