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 S
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:
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
.