This worksheet teaches students to design and run repeated chance experiments to estimate a conditional probability, and compare the simulated result to the exact theoretical value. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A simulation estimates a probability experimentally, by repeating a chance process many times and recording the relative frequency (successes ÷ total trials).
- The Law of Large Numbers: as the number of trials increases, the relative frequency converges toward the true theoretical probability — but a simulation only ever gives an estimate, with some random variation.
- To simulate a conditional probability, only count trials where the given condition is satisfied, and among those, count how many also satisfy the event of interest.
- Simulating "without replacement" (e.g. drawing marbles) requires removing each drawn item from the simulated pool before the next draw, so it cannot be drawn again.
- More trials generally give a more reliable estimate, but the amount of improvement diminishes — errors shrink, but slowly, as trials increase.
What your child will practise:
- Designing a simulation procedure (what represents each outcome, how many trials, what counts as "success") for a given probability question.
- Run/interpreting a simulation's results, converting counts into a relative frequency.
- Simulating a conditional probability by restricting to trials satisfying the given condition first.
- Comparing a simulated relative frequency to the exact theoretical probability, and explain any difference.
- Evaluating how trial count affects the reliability of a simulated estimate.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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