Simulating chance events
Design and use a simulation to estimate the probability of a compound event: choose a random device (coins, dice, spinners, counters drawn with replacement, random-digit tables, or calculator or software random numbers) and a mapping whose probabilities match the situation; define one complete trial (what is generated and when the trial stops) and the event being counted; run many trials; and estimate the probability as the event's relative frequency. Explain why the model fits (each simulated outcome has the same probability as the real one, and successive outcomes are independent when the real ones are), and why different runs give different estimates that become more consistent as the number of trials grows; where a theoretical value can be found (e.g. with a tree diagram), compare it with the estimate
Lesson
Set out your lesson
“Simulating chance events means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Tally sheet or simple bar/dot sketch
- A short set of category counts
Extra for the adult
Worked example. Cats 4, dogs 2 — cats have more. The tally and comparison are the proof.
Optional challenge. For Simulating chance events, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Simulating chance events, not mastery.
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Teaching approaches
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1 approach
Simulating chance events means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Tally sheet or simple bar/dot sketch; A short set of category counts. 1. Say the goal of Simulating chance events in plain words once. 2. Adult tallies one category and sketches a bar or dot plot. 3. Child tallies three small data sets and compares the tallest category. 4. Fresh check: one fresh tally comparison. Record and stop. Done: three correct tallies with a comparison sentence each. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
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Practice this concept
Start practiceSimulating chance events practice
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Plinko Probability
Before you open · source notes
Plinko Probability supports hands-on exploration for Simulating chance events. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Plinko Probability.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Map random digits 0–3 to 'type A' and 4–9 to 'not type A' to model donors who are type A with probability 40%, and explain why the mapping fits (4 of the 10 equally likely digits)
- Define one trial as reading digits until the first 0–3 appears, count it as a success if at least four digits were needed, run 50 trials and report the relative frequency as the estimated probability that at least four donors are needed
- Explain why two groups who each ran 50 trials estimated 0.18 and 0.26, and why pooling their trials (or running 500) gives a more reliable estimate
“If 40% of blood donors are type A, could your child use random numbers or a spinner to act out lots of donor queues, estimate how often at least four donors are needed before the first type A — and explain why doing it again gives a slightly different answer?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Probability
- Age range
- Ages 12–13
Standards