Introduction to Statistics

Experiments and Outcomes

The easiest way to think of probability is in terms of experiments and their potential outcomes. Many examples can be drawn from everyday experience: the weather today will include "rain", "overcast skies", "sun with no clouds". These are examples of outcomes from an experiment of observing weather patterns for the day. There is no implication that these outcomes are mutually exclusive. We can have "rain" in the morning followed by "sun with no clouds" in the afternoon. Perhaps a more illustrative example is to consider outcomes from drawing a card from a deck of 52. Outcomes of interest can be any of the following: "the card is a spade", "the card is a five", "the card is not a face card",...

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 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>

</math>