of the Colorado Rockies winning the pennant is high, we are stating our subjective belief
in the likelihood of that event (or perhaps engaging in wishful thinking). But when we re-
ject some hypothesis because there is a very low probability that the actual data would have
been obtained if the hypothesis had been true, it may not be important which view of prob-
ability we hold.5.2 Basic Terminology and Rules
The basic bit of data for a probability theorist is called an event.The word eventis a term that
statisticians use to cover just about anything. An event can be the occurrence of a king when
we deal from a deck of cards, a score of 36 on a scale of likability, a classification of “female”
for the next person appointed to the Supreme Court, or the mean of a sample. Whenever you
speak of the probability of something, the “something” is called an event. When we are deal-
ing with a process as simple as flipping a coin, the event is the outcome of that flip—either
heads or tails. When we draw M&M’s out of a bag, the possible events are the 6 possible col-
ors. When we speak of a grade in a course, the possible events are the letters A, B, C, D, and F.
Two events are said to be independent eventswhen the occurrence or nonoccurrence
of one has no effect on the occurrence or nonoccurrence of the other. The voting behaviors
of two randomly chosen subjects normally would be assumed to be independent, especially
with a secret ballot, because how one person votes could not be expected to influence how
the other will vote. However, the voting behaviors of two members of the same family
probably would not be independent events, because those people share many of the same
beliefs and attitudes. This would be true even if those two people were careful not to let the
other see their ballot.
Two events are said to be mutually exclusiveif the occurrence of one event precludes
the occurrence of the other. For example, the standard college classes of First Year, Sopho-
more, Junior, and Senior are mutually exclusive because one person cannot be a member
of more than one class. A set of events is said to be exhaustiveif it includes all possible
outcomes. Thus the four college classes in the previous example are exhaustive with re-
spect to full-time undergraduates, who have to fall in one or another of those categories—
if only to please the registrar’s office. At the same time, they are not exhaustive with respect
to total university enrollments, which include graduate students, medical students, nonma-
triculated students, hangers-on, and so forth.
As you already know, or could deduce from our definitions of probability, probabilities
range between 0.00 and 1.00. If some event has a probability of 1.00, then it mustoccur.
(Very few things have a probability of 1.00, including the probability that I will be able to
keep typing until I reach the end of this paragraph.) If some event has a probability of 0.00,
it is certain notto occur. The closer the probability comes to either extreme, the more likely
or unlikely is the occurrence of the event.Basic Laws of Probability
Two important theorems are central to any discussion of probability. (If my use of the word
theoremsmakes you nervous, substitute the word rules.) They are often referred to as the
additive and multiplicative rules.The Additive Rule
To illustrate the additive rule, we will use our M&M’s example and consider all six
colors. From Table 5.1 we know from the analytic definition of probability that114 Chapter 5 Basic Concepts of Probability
event
independent
events
mutually
exclusive
exhaustive