Sample space diagrams

Understanding Sample Space Diagrams

• Sample space diagrams are visual representations of all possible outcomes of a statistical experiment or random process.

• These diagrams help identify the total number of outcomes, and thus, can be utilised to determine probabilities.

• The outcomes are usually represented as points inside a geometric shape such as a square or a circle.

• Each point within the shape represents a distinct outcome.

Constructing Sample Space Diagrams

• Start by listing all the possible outcomes of the experiment.

• Use a set of axes with each outcome represented on its own axis for a two-stage experiment.

• Plot each possible outcome as a point on your grid. If it’s a two-stage experiment, the two outcomes of the first stage would typically be represented along the horizontal axis, while the outcomes of the second stage would be on the vertical axis.

• In an experiment with more than two stages or factors, consider using a three-dimensional diagram or make more complex systems of notation.

Interpreting Sample Space Diagrams

• The total number of points in the diagram typically represents the total number of possible outcomes.

• To determine the probability of a particular outcome, count the number of points that represent that outcome and divide it by the total number of points in the diagram.

• The probability of an event happening is the sum of the probabilities of all points representing the event.

• Have in mind that all probabilities in a sample space diagram should add up to 1. If they don’t, you may have missed some outcomes.

Sample Space Diagrams for Combined Events

• For experiments with more than one event, you can still use a sample space diagram but it may become more complex.

• Begin by listing the outcomes for each event on its own axis.

• To get the outcomes for the combined event, link the outcomes of the different events.