Year 9 Maths • AC9M9P03 • Authored homework
Simulations and repeated chance experiments
Design and conduct repeated chance experiments and simulations, record results, compare experimental and theoretical probabilities, and explain the effect of sample size. Show working, use correct probability language, and interpret answers in context.
Part A
Short-answer questions
What is a chance experiment?
What is a simulation in probability?
Why are repeated trials useful?
Give one example of using a random number generator to simulate an event.
What is the difference between experimental probability and theoretical probability?
Why might 10 trials give a misleading result?
What information should be recorded during a simulation?
How can technology make simulations faster?
What does it mean for results to stabilise over many trials?
Correct this error: “If the theoretical probability is 1/2, exactly half the trials must succeed.”
Part B
Long-answer questions
Design a simulation for flipping two coins and finding the probability of exactly one head. Include method, trial count and recording table.
A basketballer normally scores about 70% of free throws. Explain how to simulate 20 free throws using random digits.
Run a described simulation in theory: if 63 successes occur in 100 trials, calculate the experimental probability and compare it with 0.60.
Explain how increasing the number of trials can make experimental probability closer to theoretical probability.
Create a simulation for a game where a player wins if a die roll is 5 or 6. Predict and interpret results.
Evaluate a student’s conclusion after only 8 trials of a simulation. What should they do next?
Compare a physical experiment using dice with a digital simulation. Include advantages and limitations of each.
Design a repeated chance experiment to test whether a spinner is fair. Include data collection and decision criteria.
Use a table to show simulated results in batches of 20 trials and describe how relative frequency changes.
Write a full investigation plan for a probability simulation, including aim, model, assumptions, number of trials, table and conclusion.
Part C
Research and understanding task
Use a spreadsheet, calculator random number generator or physical materials to design a simulation for a real-life chance situation. Explain the model, run or outline repeated trials, and compare results with theoretical probability if known.