On randomness and probability: how to mathematically model uncertain events

Abstract

Whether random phenomena exist in nature or not, it is useful to think of the notion of randomness as a mathematical model for a phenomenon whose outcome is uncertain. Such a model can be obtained by exploiting the observation that, in many phenomena, even though the outcome in any given instance is uncertain, collectively there is a pattern. An axiomatic development of such a model is given below. It is also shown that in such a set-up an interpretation of the probability of an event can be provided using the 'Law of Large Numbers'.