Sample spaces

What are they?

A useful idea which relates sets and probability is the Sample Space. This is usually represented as sets of points which are then used to calculate probabilities.

Calculating conditional probabilities can be achieved by indentifying the required outcomes from the reduced sample space. For example, suppose that we wish to calculate the probability of randomly choosing a domino containing at least six from a regular twenty-eight set. Seven of the twenty-eight sample points contain a six.

Probability (choosing a six) = 7/28 = ΒΌ = 0.25 = 25%

Below is an application involving rolling two dice, calculating the probability of rolling a given number (between 2 and 12) Click on application to start rolling dice:

Applet courtesy of