Abstract
Probability as a concept has been associated with strong and often diverging opinions amongst experts, particularly within the field of mathematics. The present chapter, comprising Lecture 2, therefore starts out with a short introduction to the different leading interpretations of probability and explains how the Bayesian interpretation of probability may appropriately envelope and accommodate for the other interpretations in the context of engineering decision making. Thereafter, the basic concepts, such as sample space and events, from set theory are introduced and the mathematical foundation of probability theory is provided through the introduction of the three axioms of probability theory. With this basis the concept of conditional probability is introduced and one of the most central results for modern probability and decision theory is derived, namely the rule of Bayes. This important result forms the mathematical framework for synthesizing information into knowledge. The chapter is concluded by two examples illustrating how the rule of Bayes may be applied to quantify the knowledge acquired by collection of information in the context of condition and load carrying capacity assessments of concrete structures.
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