In the field of Safety Engineering, probabilistic and deterministic mathematical representations are used to calculate how likely an event may occur, which could lead to a major hazard. Although there are several different interpretations, probability theory treats the concept in a rigorous mathematical manner, by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.

1. Basic theoretical probability

2. Probability using sample spaces

3. Basic set operations

4. Experimental probability

5. Randomness, probability, and simulation