What is a probability? What does it mean to say that a probability of a fair coin is one half, or that the chances I pass this class are 80 percent, or that the probability that the Steelers win the Super Bowl this season is .1?

First, think of some event where the outcome is uncertain. Examples of such outcomes would be the roll of a die, the amount of rain that we get tomorrow, the state of the economy in one month, or who will be the President of the United States in the year 2001. In each case, we don't know for sure what will happen. For example, we don't know exactly how much rain we will get tomorrow.

A * probability * is a numerical measure of the likelihood of the event. It is a number that we attach to an event, say the event that we'll get over an inch of rain tomorrow, which reflects the likelihood that we will get this much rain.

A probability is a number from 0 to 1. If we assign a probability of 0 to an event, this indicates that this event * never * will occur. A probability of 1 attached to a particular event indicates that this event * always * will occur. What if we assign a probability of .5? This means that it is just as likely for the *
event to occur * as for the event * to not occur. *

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```
THE PROBABILITY SCALE
+----------------------------+----------------------------+
0 .5 1
event never event and "not event" always
will occur event are likely will occur
to occur
```

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There are two basic interpretations, or ways of thinking, about probabilities. These interpretations will help us assign probabilities to uncertain outcomes.

Return to AN INTRODUCTION TO PROBABILITY

Page Author: Jim Albert (© 1996)

albert@bayes.bgsu.edu

Document: http://www-math.bgsu.edu/~albert/m115/probability/interp.html

Last Modified: November 18, 1996