## THE SUBJECTIVE INTERPRETATION OF PROBABILITY

The relative frequency notion of probability is useful when the process of interest, say tossing a coin, can be repeated many times under similar conditions. But we wish to deal with uncertainty of events from processes that will occur a single time. For example, you are likely interested in the probability that you will get an A in this class. You will take this class only one time; even if you retake the class next semester, you won't be taking it under the same conditions as this semester. You'll have a different instructor, a different set of courses, and possibly different work conditions. Similarly, suppose you are interested in the probability that BGSU wins the MAC championship in football next year. There will be only a single football season in question, so it doesn't make sense to talk about the proportion of times BGSU would win the championship under similar conditions.

In the case where the process will happen only one time, how do we view probabilities? Return to our example in which you are interested in the event "get an A in this class". You assign a number to this event (a probability) which reflects your personal belief in the likelihood of this event happening. If you are doing well in this class and you think that an A is a certainty, then you would assign a probability of 1 to this event. If you are experiencing difficulties in the class, you might think "getting an A" is close to an impossibility and so you would assign a probability close to 0. What if you don't know what grade you will get? In this case, you would assign a number to this event between 0 and 1. The use of a calibration experiment is helpful for getting a good measurement at your probability.

• A subjective probability reflects a person's opinion about the likelihood of an event. If our event is "Joe will get an A in this class", then my opinion about the likelihood of this event is probably different from Joe's opinion about this event. Probabilities are personal and they will differ between people.

• Can I assign any numbers to events? The numbers you assign must be proper probabilities. That is, they must satisfy some basic rules that all probabilities obey. Also, they should reflect your opinion about the likelihood of the events.

• Assigning subjective probabilities to events seems hard. Yes, it is hard to assign numbers to events, especially when you are uncertain whether the event will occur or not. We will learn more about assigning probabilities by comparing the likelihoods of different events. Return to AN INTRODUCTION TO PROBABILITY

Page Author: Jim Albert (© 1996)
albert@bayes.bgsu.edu
Document: http://www-math.bgsu.edu/~albert/m115/probability/subject.html