L01.3 Sample Space Examples

Introduction to Sample Spaces

In this section, the concept of sample spaces is introduced. Sample spaces can be discrete, finite, infinite, continuous, etc.

Discrete and Finite Sample Space

• A tetrahedral die with four faces numbered from 1 to 4 is rolled twice in a single probabilistic experiment.

• The sample space for this experiment can be represented as pairs of numbers corresponding to the results of each roll.

Order Matters in Sample Space

• Different outcomes occur when the order of the numbers in the pair changes.

• The order in which the numbers appear may be of interest and should be considered as separate outcomes.

Describing Experiments with Multiple Stages

This section discusses experiments that can be described in phases or stages using a sequential description in terms of a tree diagram.

Tree Diagram Representation

• A tree diagram is a useful way to describe experiments with multiple stages.

• The root represents the start of the experiment, and the leaves represent possible outcomes.

• Each branch represents a stage or phase of the experiment.

Discrete and Infinite Sample Spaces

This section explores sample spaces that are discrete and finite as well as those that are infinite and continuous.

Example of Continuous Sample Space

• An experiment involves throwing a dart at a unit square target.

• The coordinates (x, y) of the point where the dart lands on the target are recorded.

• The sample space for this experiment is continuous since there are infinitely many possible points within the unit square.

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