ABSTRACT
The key point of the previous chapter is that the properties of a 'proba-
bility function' seem to play a more important role than the definition of
probability itself. More specifically, from a mathematical point of view we
are led to the idea that the way in which we assign probabilities to events is
almost secondary with respect to the fact that these probabilities must satisfy
a number of well-defined properties. Therefore, by temporarily ignoring the
way in which we assign probabilities to events - but, at the same time, by
defining what exactly is meant by 'event' - we can simply define a 'proba-
bility function' as something that satisfies a given set of rules. By so doing,
each one of the definitions given in Chapter 1, the classical definition, the
relative frequency definition, etc., turns out to be just a special case of 'prob-
ability function' which works perfectly well in the appropriate context. So,
in fair games of chance (dice, roulette, lotteries, etc.) we adopt the classical
probability, in repeated experiments where the classical definition cannot be
used (mortality rates, measurement of a physical quantity, etc.), we turn to
the relative frequency definition of probability, etc.
