Risk Assessment: Tools, Techniques, and Their Applications

7.2 Probability Theory

Probability is defined as the likelihood that the event will occur. Probability measures the uncertainty associated with the outcomes of a random experiment. Some other terms or words used in place of probability are chance, likelihood, uncertainty, and odds. Probability is usually expressed as a fraction with the denominator representing the total number of ways things can occur and the numerator representing the number of things that you are hoping will occur. Probability is always a number between 0 and 1 or between 0% and 100%. Zero means that something cannot happen (impossible) and 1 or 100% means it is sure to happen. Another way to express this is 0 ≤ P(A) ≤ 1, where A is the event. This expression is the first basic rule of probability (3).

There is also a rule that applies to two events, A and B, which are mutually exclusive, that is, the two events cannot occur at the same time. In this case, we express this as P(A or B) = P(A) + P(B). Some textbooks will use mathematical symbols for the words “and” and “or” and the expression would look like .

Although these rules of probability are extremely few and simple, they are incredibly powerful in application. In order to understand probability, you must know how many possible ways a thing can happen. For instance, if you flip a coin, there are two possible ways it can land, either heads or tails. If we ...