Investigating chance with a simulation (internal)
Internal 2 credits Simulation Random numbers Trials Estimating probability VariabilityAS 91268, 2 credits. Estimate a probability that is awkward to calculate directly, by simulating it. The standard requires evidence of using each component of the simulation process; Merit links those components to the context.
1 Reading the notation
Design is planned BEFORE running trials — including how results will be recorded.📖 Terms the schedule grades you on
3 terms- Investigate (Achieved)
- Evidence of using EACH component of the simulation process.
- With justification (Merit)
- Link components to context; explain design considerations; support findings with evidence from the simulation.
- With statistical insight (Excellence)
- Integrate statistical and contextual knowledge throughout — reflecting on process, or considering other variables.
2 Designing the simulation
Tool, assignment, and the definition of one trial — the whole simulation depends on getting these right. Internal-style A player makes 70% of free throws. What is P(at least 4 of 5)? Design the simulation. TOOL: single random digits 0–9. ASSIGNMENT: 0–6 = made (7 of 10 = 70%); 7–9 = missed. ONE TRIAL: read five digits; count the makes. EVENT OF INTEREST: a trial with 4 or 5 makes. NUMBER OF TRIALS: 200, run with technology so the estimate stabilises. ✓ Every component stated explicitly. The assignment 0–6 / 7–9 is what makes the simulation reproducible by someone else.3 Calculating and interpreting the estimate
It is an estimate, not the true probability — and variability is part of the answer, not a caveat. ✕Reporting the estimate with false precision
An estimate from 50 trials reported to three decimal places (e.g. 0.684) claims a precision the simulation cannot support. Round sensibly, and say how many trials it is based on.4 What each grade requires
Justification links design choices to the situation; insight integrates throughout.| Grade | What it takes | The half people drop |
|---|---|---|
| Achieved | Evidence of using EACH component of the process | Missing one component entirely — every one needs visible evidence |
| Merit ("with justification") | Link components to the context; support findings with evidence from the work | Asserting a decision instead of explaining WHY, for this context |
| Excellence ("with statistical insight") | Integrate statistical and contextual knowledge THROUGHOUT | Treating it as one closing paragraph rather than woven through every component |
"With statistical insight" often means reflecting on the process itself, or naming another variable/explanation the data cannot rule out.
Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.