Introduction to Statistics

Experiments, Outcomes and Events

The easiest way to think of probability is in terms of experiments and their potential outcomes. Many examples can be drawn from everyday experience: On the drive home from work, you can encounter a flat tire, or have an uneventful drive; the outcome of an election can include either a win by candidate A, B, or C, or a runoff.

Definition: The entire collection of possible outcomes from an experiment is termed the sample space, indicated as <math>\Omega</math>

The simplest (albeit uninteresting) example would be an experiment with only one possible outcome, say <math>A</math>. If we remember our set theory from elementary school, we can expressed the sample space as follows:

<math>\Omega = \{ A \} </math>

A more interesting example is the result of rolling a six sided dice. The sample space for this experiment is:

<math>\Omega = \{ 1,2,3,4,5,6 \}</math>

We may be interested in events in an experiment.

Definition: An event is some subset of outcomes from the sample space

In the dice example, events of interest might include
a) the outcome is an even number
b) the outcome is less than three

These events can be expressed in terms of the possible outcomes from the experiment:
a) : <math> \{2,4,6\} </math> b) <math> \{ 1,2 \}</math>

We can borrow definitions from set theory to express events in terms of outcomes. Here is a refresher of the terminology:
<math> \cup </math> represents the Union of two events
[[Image:[1]]]
<math> \cap </math> represents the Interection of two events
[[Image:[2]]]