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 in context what it means for two events to be independent. (Guide: “What does ‘independent’ mean?”)
- I can state the three equivalent conditions for independence and explain why checking one is enough. (Guide: “Three ways to check for independence”)
- I can explain why P(A ∩ B) is subtracted in the general addition rule, using a Venn diagram. (Guide: Figure 1; Practice Q1)
- I can explain why mutually exclusive events with non-zero probabilities cannot be independent. (Guide: Worked example 3; Practice Q7(c))
- I can explain why past results of independent trials do not change the next result. (Practice Q7(b))
Calculation
- I can check independence from a two-way table by comparing P(A | B) with P(A), showing both values. (Guide: Worked example 1; Practice Q4)
- I can check independence from given probabilities, including finding P(A ∩ B) from P(A ∪ B). (Practice Q2, Q6)
- I can use P(A ∩ B) = P(A) · P(B) for independent events, including more than two events. (Guide: Worked example 2; Practice Q5, Q7(a))
- I can calculate P(A ∪ B) with the general addition rule and check it with 1 − P(neither). (Guide: Worked examples 1 and 2; Practice Q4, Q6)
- I can find the probability of at least one success in several independent trials with 1 − P(none). (Guide: Worked example 2; Practice Q3)
Reasoning
- I can judge whether an independence assumption is reasonable in context, and say what changes if it is not. (Guide: Worked example 2; Practice Q5(c))
- I can show every probability calculation as rule, substituted values and answer, and interpret the result in context. (All worked examples)
All ticked? Move on to Topic 2.8, Introduction to Random Variables and Probability Distributions, or return to the course roadmap.