- explain the central idea: Design repeated chance experiments and digital simulations for conditional probability, then interpret long-run results and model limitations.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
Year 10 Mathematics · AC9M10P02
Conditional Probability Experiments and Simulations
Design a simulation that matches the real dependency and replacement rules, repeat it enough times to stabilise frequencies, then interpret variation and limitations…
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
Simulation approximates probability using repeated trials. The model must preserve sample space, conditional structure and whether sampling is with/without replacement. Larger trial counts usually reduce random fluctuation in relative frequency.
Relative frequency
successes/trials.
Design
Map random outcomes to real outcomes with correct probabilities.
Dependence
Update probabilities after outcomes when the real process changes.
Reliability
Repeat many trials, compare runs and state model assumptions/limitations.
Worked examplesWe do
Worked examples
AC9M10P02 - Conditional Probability Experiments and Simulations
Example 1
Relative frequency successes/trials.
Example 2
Design Map random outcomes to real outcomes with correct probabilities.
Example 3
Dependence Update probabilities after outcomes when the real process changes.
Example 4
Reliability Repeat many trials, compare runs and state model assumptions/limitations.
Curriculum examplesCopied content
Australian Curriculum: AC9M10P02 — Year 10 Probability. Design repeated chance experiments and digital simulations for conditional probability, then interpret long-run results and model limitations.
Victoria: VC2M10P01 and VC2M10P02 — Level 10 Probability; the first explicitly includes conditional-probability simulation
NSW: Stage 5 Core — Probability; Path — Further probability
Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.
| Lesson component | Australian Curriculum | Victoria | NSW |
|---|---|---|---|
| Explicit concept teaching and worked examples | AC9M10P02 | VC2M10P01 and VC2M10P02 — Level 10 Probability; the first explicitly includes conditional-probability simulation | Stage 5 Core — Probability; Path — Further probability |
| Guided and independent practice | Builds fluency and application for AC9M10P02 | Practises the mapped Level 10/10A knowledge as applicable | Practises the mapped Stage 5 Core/Path content |
| Reasoning and assessment tasks | Applies reasoning/problem solving in the descriptor context | Supports Victorian reasoning and modelling expectations | Embeds Working mathematically: reasoning, problem solving and communication |
Australian Curriculum elaborations
AC9M10P02: design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results.
- E1: compare different sample sizes with/without replacement and when difference becomes negligible. Examples 2–4.
- E2: recognise dependency affects probability calculation. Example 3.
- E3: use simulations for counter-intuitive chance situations such as three-door/birthday problems. Examples 5–6.
- E4: identify real-life simulation decision uses such as supply-demand, insurance and queueing. Examples 7–8.
- E5: use simulation to predict likely infection numbers for flu/virus contexts. Example 9, with explicit model limitations.
Questions and answersWith answers
- Find relative frequency 420/600.
- 0.7.
- Does replacement make repeated bag draws independent if composition returns exactly?
- Yes, if each draw resets same probabilities.
- Bag 5R,5B: after red without replacement, P(next red)?
- 4/9.
Practice and reviewReady for practice
- Using equal random outcomes for unequal real probabilities.
- Forgetting to update probabilities without replacement.
- Believing more trials fix a wrong model.
- Reporting one simulation run as exact probability.
- Changing a counter-intuitive problem's rules during simulation.
Curriculum alignmentStart here
- explain the central idea: Design repeated chance experiments and digital simulations for conditional probability, then interpret long-run results and model limitations.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
- Australian Curriculum Version 9 — ACARA
- Victorian Curriculum Mathematics Version 2.0 — VCAA
- NSW Mathematics K–10 Syllabus (2022) — NSW Curriculum/NESA
Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.
Other curriculum comparisons retained
US closest CCSS HSS-CP and HSS-IC simulation standards; UK GCSE conditional probability/relative frequency; NSW Stage 5 and Victorian Level 10 probability; comparable Canadian/NZ simulations.
Teach & ExplainTeaching slides and samples
Teach this topic step by step
Explore optional teaching slide packs for classroom lessons and explanations at home.
Browse Teach & Explain · Browse Print & Go
Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.
After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.