1.2 Interpretations  (Page 3/5)

Subjective probability and a football game

The probability that one's favorite football team will win the next Superbowl Game may well be only a subjective probability of the bettor. This is certainlynot a probability that can be determined by a large number of repeated trials. The game is only played once. However, the subjective assessment of probabilitiesmay be based on intimate knowledge of relative strengths and weaknesses of the teams involved, as well as factors such as weather, injuries, and experience. There maybe a considerable objective basis for the subjective assignment of probability. In fact, there is often a hidden “frequentist” element in the subjective evaluation.There is an assessment (perhaps unrealized) that in similar situations the frequencies tend to coincide with the value subjectively assigned.

The probability of rain

Newscasts often report that the probability of rain of is 20 percent or 60 percent or some other figure. There are several difficulties here.

• To use the formal mathematical model, there must be precision in determining an event. An event either occurs or it does not. How do wedetermine whether it has rained or not? Must there be a measurable amount? Where must this rain fall to be counted? During what time period?Even if there is agreement on the area, the amount, and the time period, there remains ambiguity: one cannot say with logical certainty the event did occur orit did not occur. Nevertheless, in this and other similar situations, use of the concept of an event may be helpful even if the description is notdefinitive. There is usually enough practical agreement for the concept to be useful.
• What does a 30 percent probability of rain mean? Does it mean that if the prediction is correct, 30 percent of the areaindicated will get rain (in an agreed amount) during the specified time period? Or does it mean that 30 percent of the occasions on which such aprediction is made there will be significant rainfall in the area during the specified time period? Again, the latter alternative may well hide afrequency interpretation. Does the statement mean that it rains 30 percent of the times when conditions are similar to current conditions?

Regardless of the interpretation, there is some ambiguity about the event and whether it has occurred. And there is some difficulty with knowinghow to interpret the probability figure. While the precise meaning of a 30 percent probability of rain may be difficult to determine, it isgenerally useful to know whether the conditions lead to a 20 percent or a 30 percent or a 40 percent probability assignment. And there is no doubt that asweather forecasting technology and methodology continue to improve the weather probability assessments will become increasingly useful.