Introducing Probability

Abstract

Probability is a universally accepted tool for expressing degrees of confidence or doubt about some proposition in the presence of incomplete information or uncertainty. By convention, probabilities are calibrated on a scale of 0 to 1; assigning something a zero probability amounts to expressing the belief that we consider it impossible, while assigning a probability of one amounts to considering it a certainty. Most propositions fall somewhere in between. For example, if someone pulls out a coin and asks if the coin will show heads when tossed once, most of us will be inclined to say that the chances of the coin showing heads are 50%, or equivalently .5. On the other hand, if someone asks what the chances are that gravity will cease to exist tomorrow, we will be inclined to say that the chances of that are zero. In these two examples, we assign the chances .5 and 0 to the two propositions because in our life experience we have seen or heard that normal coins tend to produce heads and tails in roughly equal proportions and also that, in the past, gravity has never ceased to exist.