THE MEANING OF PROBABILITY

The single term ‘probability’ can be used in several distinct senses. These fall into two main groups. A probability can be a limiting ratio in a sequence of repeatable events. Thus the statement that a coin has a 50% probability of landing heads is usually taken to mean that approximately half of a series of tosses will be heads, the ratio becoming ever more exact as the series is extended. But a probability can also stand for something less tangible: a degree of knowledge or belief. In this case, the probability can apply not just to sequences, but also to single events. The weather forecaster who predicts rain tomorrow with a probability of ½ is not referring to a sequence of future days. He is concerned more to make a reliable forecast for tomorrow than to speculate further ahead; besides, the forecast is based on particular atmospheric conditions that will never be repeated. Instead, the forecaster is expressing his confidence of rain, based on all the available information, as a value on a scale on which 0 and 1 represent absolute certainty of no rain and rain respectively.

The former is called the frequency interpretation of probability, the latter the epistemic or ‘degree of belief’ or Bayesian interpretation, after the Reverend Thomas Bayes, an eighteenth-century writer on probability.