Let us now be more precise about our terminology and define some
additional terms that lead to the concept of a pdf.
Consistent with standard textbooks (e.g., [Hamming] or [DeGroot]), we will
refer to the physical or
mathematical process as an experiment, and this experiment has a number
(possibly infinite) of outcomes, to which we will assign probabilities.
The sample space 
of the experiment is the collection of all
possible outcomes 
.
Thus if the experiment is carried out, its outcome is assured to be in the
sample space .
We will also describe one realization of the experiment as a trial,
and by definition a trial will have an outcome in the sample space .
The experiment may result in the occurrence of a specific event 
.
An event may
be viewed as a consequence of the outcome (or outcomes) of the experiment.
Let us now illustrate these concepts with a simple example.
The experiment consists of one roll of a normal die (with
faces labeled 1, 2, 3, 4, 5, and 6) and observing the top face of the
die. The outcomes 
are the six faces, and the sample space
consists of these six outcomes, since every realization of the
experiment (i.e., each trial) results in one of these faces being the top face.
(We will assume that the die will not balance on an edge or corner.)
Events can then be defined in terms of the possible outcomes.
Possible events that may be defined in terms of the six unique
outcomes are:
: top face is an even number
: top face is larger than 4
: top face is equal to 2 (hence the event is one of the outcomes)
Disjoint events are events that cannot happen at the same time.
In the above
example, events and are disjoint, because a single roll of the die
(as the experiment was defined) cannot lead to both events occurring.
On the other
hand, events and can occur at the same time, as can events
and .