Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain what a random process, a trial, an outcome and an event are, with an example of each. (Guide: “Random processes, outcomes and events”; Practice Q1)
- I can explain probability as the relative frequency of an event over a very large number of trials. (Guide: “Probability as long-run relative frequency”)
- I can explain why a relative frequency from data or a simulation is only an estimate of the true probability. (Guide: Worked example 2; Practice Q7)
- I can state the law of large numbers and explain why it says nothing about the next trial. (Guide: “The law of large numbers”; Practice Q3, Q7)
Skills
- I can assign single digits, pairs of digits or random integers to outcomes so that the probabilities match the real situation. (Guide: “Designing a simulation”; Practice Q2, Q6)
- I can describe one trial of a simulation and say what to record. (Practice Q5, Q6)
- I can carry out trials from a line of random digits, allowing repeats when the parts of a trial are independent. (Guide: Worked example 1; Practice Q4)
- I can carry out trials without replacement, skipping a value that repeats within a trial. (Guide: Worked example 2; Practice Q5)
- I can estimate a probability as count ÷ total from a table of simulation results, and use it to estimate an expected number. (Practice Q5, Q6)
Reasoning
- I can judge which of two simulation estimates is more reliable, using the number of trials. (Practice Q7)
- I can explain why the “law of averages” is wrong for independent trials. (Guide: “Common misconceptions”; Practice Q3, Q7)
- I can write a conclusion to a simulation in context, with the count, the total and the estimate. (All worked examples)
All ticked? Move on to Topic 2.4: Introduction to Probability, or return to the course roadmap.