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9 exam-style questions with model answers, plus 9 quick multi-choice questions — every question on the site for this standard, grouped by the 3 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
A spinner lands on red with probability 0.5. Using one random digit (0–9), assign digits to model one spin.
35% of eggs in a carton are free-range. Design an assignment and a trial to simulate the number of free-range eggs in a box of 6.
A cereal brand puts one of 4 equally likely collectable cards in each box. Design a simulation to estimate the probability that a child collects all 4 different cards within their first 5 boxes.
In 50 simulated trials, an event happened 18 times. Estimate its probability.
A simulation of the number of rainy days in 3 days gave: 0 days ×72, 1 day ×86, 2 days ×34, 3 days ×8 (200 trials). Estimate the probability of rain on at least 2 of the 3 days.
From the same simulation, a student estimates P(at least 2 rainy days) = 0.21. The true theoretical value is 0.352. Suggest why the estimate differs and how to improve it.
Why does a simulation with 500 trials usually give a better estimate than one with 10 trials?
Two students simulate the same event. One runs 20 trials and gets 0.15; the other runs 400 and gets 0.23. Whose estimate should you trust more, and why?
A student says 'to get a better estimate of the probability of at least 4 makes in 5 shots, I'll make each trial 20 shots instead of 5.' Explain why this does not help, and what they should do instead.