How to teach sample space and probability experiments
Year 7 (ages 12 to 13)
The sample space is the full list of possible outcomes of a chance event. This unit covers listing a sample space, finding probabilities as fractions from it, and comparing a real experiment's results with what theory predicts.
How to teach it
- Start by listing the full sample space for a simple event (a die, a spinner), counting the total number of equally likely outcomes.
- Find a probability as a fraction: favourable outcomes divided by the total in the sample space, simplifying where possible.
- Run (or simulate) a real experiment with many trials, and calculate the relative frequency of an outcome from the actual results.
- Compare the relative frequency with the theoretical probability, discussing why they are close but not necessarily identical.
- Increase the number of trials and observe that the relative frequency usually settles closer to the theoretical probability.
Worked example
A fair 6-sided die is rolled once
Sample space: {1, 2, 3, 4, 5, 6}, 6 equally likely outcomes
P(rolling an even number) = 3/6 = 1/2Common mistakes
- Listing an incomplete sample space, missing possible outcomes.
- Assuming all listed outcomes are equally likely without checking (e.g. a weighted spinner).
- Expecting an experiment's relative frequency to exactly match the theoretical probability every time.
- Not simplifying a probability fraction to its lowest terms.
Frequently asked questions
What is a sample space?
The sample space is the complete list of all possible outcomes of a chance event. Rolling a six-sided die has the sample space {1, 2, 3, 4, 5, 6}, six equally likely outcomes.
How do you find the probability of an outcome from the sample space?
Count the favourable outcomes and divide by the total number of outcomes in the sample space. The probability of rolling an even number on a six-sided die is 3/6 = 1/2, since 3 of the 6 outcomes are even.
What is the difference between theoretical probability and an experiment's result?
Theoretical probability is calculated from the sample space by reasoning; an experiment's relative frequency comes from actually running trials and counting results. They are usually close but rarely identical, due to natural chance variation.
What year are sample space and probability experiments taught?
In the Australian Curriculum both are Year 7 skills: listing the sample space and assigning probabilities (AC9M7P01), and running experiments/simulations and comparing predicted with observed results (AC9M7P02).
Practise with free worksheets
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