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 sample space is and why P(S) = 1. (Guide: “The sample space”; Practice Q4)
- I can explain why every probability lies from 0 to 1, and what 0 and 1 mean. (Guide: “The basic rules”; Practice Q1)
- I can explain the difference between a theoretical probability and an estimate from a simulation. (Guide: “From estimates to exact probabilities”)
- I can explain what the complement of an event is and read the notations Eᶜ, E′ and Ē. (Guide: “The complement of an event”)
Calculation
- I can list the sample space of a one-stage or two-stage random process, using a grid or a systematic list. (Guide: Figure 1 and Worked example 2(a); Practice Q6(a))
- I can calculate P(E) by counting when all outcomes are equally likely. (Guide: Worked example 1; Practice Q3, Q6)
- I can find the probability of choosing a category when one individual is chosen at random from a table of counts. (Guide: “Probabilities when outcomes are equally likely”; Practice Q5)
- I can find a missing probability using the fact that the probabilities of all outcomes add to 1. (Guide: “The basic rules”; Practice Q4)
- I can use P(Eᶜ) = 1 − P(E), including P(at least one) = 1 − P(none). (Guide: Worked example 2; Practice Q2, Q6)
Reasoning
- I can decide whether outcomes are equally likely before I count them, and explain why counting fails when they are not. (Guide: Worked example 1(d); Practice Q3, Q5(d), Q7(a))
- I can describe the complement of an event in words, such as “at most 1” for “at least 2”. (Guide: complement table; Practice Q7(b))
- I can use the 0-to-1 rule and the fact that P(S) = 1 to spot an impossible answer and explain the error. (Practice Q4(c), Q7(c))
All ticked? Move on to Topic 2.5: Mutually Exclusive Events, or return to the course roadmap.