Year 8 Mathematics · AC9M8P03

Compound Chance Experiments and Simulations

Use repeated trials and well-designed digital simulations to estimate probabilities for compound events, compare relative frequency with theoretical probability, and…

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Key conceptTeach from the board

A compound event involves more than one component, such as two coin tosses or two dice. A simulation must reproduce the rules of the actual chance process: possible outcomes, probabilities, replacement/dependence assumptions and the number of stages.

Experimental probability is measured by relative frequency = favourable trials ÷ total trials. It varies from run to run. With more trials, results often settle closer to the theoretical probability, but there is no requirement that a finite simulation equal the theoretical value exactly.

Digital tools—including random-number generators and, where appropriate, generative AI used to help construct or run a simulation—must be checked. The mathematics is not trustworthy merely because software produced it. Verify outcome coding, randomisation rules and what counts as a favourable event.

A useful Year 8 investigation is rolling two dice and studying the absolute difference between them. Some differences occur more often because different numbers of ordered pairs produce them. Another is testing complementary events in a long-run simulation and checking whether their relative frequencies add to approximately 1.

Worked examplesWe do

Worked examples

AC9M8P03 - Compound Chance Experiments and Simulations
Example 1

List the sample space for two fair coin tosses and find P(two heads).

Example 2

A simulation gives 126 successes in 300 trials. Calculate relative frequency.

Example 3

Explain two checks needed before trusting a digital two-dice simulation.

Example 4

Compare 30-trial and 3000-trial simulation results: which would you usually expect to be more stable and why?

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8P03: conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8P03:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-PRO-C-01; MAO-WM-01:Supporting. Current Stage 4 probability focuses on simple chance experiments; multistage chance and simulations are developed more explicitly later in the NSW sequence.

LessonAC v9VictoriaNSW
Compound chance simulationsAC9M8P03VC2M8P03 — ExactMA4-PRO-C-01; MAO-WM-01 — Supporting
Questions and answersWith answers
  1. What is experimental probability? Relative frequency from observed or simulated trials.
  2. Why use many trials? To reduce the impact of short-run random fluctuation and obtain a more stable estimate.
  3. Does a simulation prove the theoretical probability? No; theory comes from the probability model, while simulation provides empirical evidence.
  4. What must be checked in a digital simulation? Outcome rules, randomisation, probabilities, stage/dependence assumptions and event coding.
Practice and reviewReady for practice
  • 1000 trials must give the exact theoretical probability. Random variation remains in finite samples.
  • A digital simulation is automatically valid. Check coding, probabilities and dependence/replacement rules.
  • More trials change the theoretical probability. They change the stability of the estimate, not the underlying model probability.
  • All two-dice derived outcomes are equally likely. A derived value can have different numbers of ordered pairs producing it.
Curriculum alignmentStart here
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