Reasoning with risk: Teaching probabili...

Risk is a key aspect of life and probability is the mathematical tool to address risk. Our aim is to investigate how risk is embedded in probability and how probability can be used to solve problems of risk. Furthermore, we illustrate how risky situations are paradigmatic for the concept of probability, not least by the eminent role risk played for the emergence of probabilistic concepts. The analysis of risk forms the central section, which shows how risk is connected to probability. Decisions in risky situations draw from the various approaches to probability and from rational and behavioural views to decisions. The section on emerging concepts re-visits the development of probability and probabilistic thinking. Faced with the twin character of probability and risk, we argue that these concepts should be developed together in teaching. The conceptualisation of probability in terms of A Priori Theory (APT) Frequentist Theory (FQT) and Subjectivist Theory (SJT) forms the background to classify the pertinent constituents of the arguments. For understanding small probabilities/risks, we promote the ideas of a micromort (1 in a million chance of leading to death) and a microlife (a half-hour period, which is 1 in a million part of the average life span of a person aged 30 years).

 Keywords: A priori probability theory; Freq