## Probability

In everyday conversations about different possibilities, these are often compared as being equally, or more, or less likely —or probable —than others. Risk researchers and practitioners often treat the probability of some event as a number between 0 and 100. They then apply the rules for mathematical probabilities to these numbers. If a possibility appears again and again, the probability that it will be realized is often seen as the limiting value that one would get by counting the cases where it has been realized and dividing it by the number of occasions where the possibility did arise. Economists and decision analysts often use the word ‘‘probability’’ to characterize the willingness of an agent to engage in a bet with well defined stakes. Leaving one’s home without an umbrella is then seen as equivalent to betting that it will not rain, where the stakes depend on one’s clothes and further circumstances. Mathematicians use the word ‘‘probability’’ for functions that associate real numbers to certain subsets of a set while satisfying the rules known as the Kolmogorov axioms. An example is a function that associates to any number of fields on a chessboard that number divided by 64: the whole chessboard has a probability of 1, a single row or column a probability of 1/8, a single field has probability 1/64, etc.