Marvin Rausand - Risk Assessment

An accident arising from component failures, including the possibility of multiple and cascading failures (e.g. see Leveson 2004).

To answer the second question in the triplet definition of risk,“What is the likelihood of that happening?” we need to use concepts from probability theory. A brief introduction to probability theory is given in Appendix A. Essentially, the probability of an event is a number between 0 and 1 (i.e. between 0% and 100%) that expresses the likelihood that the event occurs in a specific situation, and is written as . If , we know with certainty that event occurs, whereas for , we are certain that event will not occur.

Probability is a complex concept about whose meaning many books and scientific articles have been written. There are three main approaches to probability: (i) the classical approach, (ii) the frequentist approach, and (iii) the Bayesian or subjective approach.

People have argued about the meaning of the word “probability” for at least hundreds of years, maybe thousands. So bitter, and fervent, have the battles been between the contending schools of thought, that they've often been likened to religious wars. And this situation continues to the present time (Kaplan 1997 , p. 407).

The classical approach to probability is applicable in only a limited set of situations, where we consider experiments with a finite number of possible outcomes, and where each outcome has the same likelihood of occurring. This is appropriate for many simple games of chance, such as tossing coins, rolling dice, dealing cards, and spinning a roulette wheel.

We use the following terminology: An outcome is the result of a single experiment, and a sample space is the set of all the possible outcomes. An event is a set of (one or more) outcomes in that have some common properties. When an outcome that is a member of occurs, we say that the event occurs. These and many other terms are defined in Appendix A.

Because all possible outcomes have the same likelihood of occurring, we can find the likelihood that event will occur as the number of outcomes that belong to divided by the number of possible outcomes. The outcomes that belong to are sometimes called the favorable outcomes for . The likelihood of getting an outcome from the experiment that belongs to is called the probability of :

(2.1)

The event can also be a single outcome. The likelihood of getting a particular outcome is then called the probability of the outcome and is given by .

When – as in this case – all the outcomes in have the same probability of occurrence, we say that we have a uniform model.

The frequentist approach restricts our attention to phenomena that are inherently repeatable under essentially the same conditions. We call each repetition an experiment and assume that each experiment may or may not give the event . The experiment is repeated times as we count the number of the experiments that end up in the event . The relative frequency of is defined as

Because the conditions are the same for all experiments, the relative frequency approaches a limit when . This limit is called the probability of and is denoted by