Introduction to probability theory

Certainty is what dissappears when you begin to understand a problem.

Nicolas Deichmann

A common way to describe uncertainties, independent of their nature, is in terms of probabilities. Challenging in the  context of modern probabilistic hazard analysis is the fact that different interpretations regarding the meaning of  probability are used in combination. Although this might seem counterintuitive at first glance, this combination of concepts is one pillar of the foundations of PSHA. Under conditions which are discussed below (Kolmogorovs axioms) this is completely acceptable. The current section is not a comprehensive  discussion of all possible probability concepts but focused on those which are essential to obtain a conceptual understandig of modern probabilistic hazard analysis.  

Frank Scherbaum (2015), Fundamental concepts of Probabilistic Seismic Hazard Analysis, Hazard Classroom Contribution No. 001