Statistics Foundation · Lesson 3.4
Independence and dependence.
Independence and dependence describe whether one event changes the probability of another. This lesson develops the idea using conditional probability, joint probability, two-way tables, tree diagrams and repeated-trial examples.
Lesson route
Move from conditional probability to independence checks.
Students now use conditional probability as a diagnostic tool: does knowing one event change another probability, or does the probability remain unchanged?
0–10 min
What dependence means
Understand that events are dependent when knowing one event changes the probability of another.
10–25 min
Conditional probability connection
Use P(A | B) to decide whether event B changes the probability of event A.
25–45 min
Definition of independence
Learn that A and B are independent when P(A | B) = P(A), provided P(B) > 0.
45–65 min
Multiplication rule
Derive P(A ∩ B) = P(A)P(B) for independent events.
65–90 min
Tables and visual checks
Use two-way tables, Venn diagrams and conditional proportions to detect dependence.
90–115 min
Common misconceptions
Distinguish independence from disjointness, causation and unrelated-looking events.
Mastery checklist
Students should be able to decide whether information changes probability.
Define independence using conditional probability.
Define dependence using changed probability.
Use P(A ∩ B) = P(A)P(B) as an independence check.
Explain why disjoint events are usually dependent.
Use two-way tables to compare conditional proportions.
Distinguish sampling with replacement from without replacement.
Avoid confusing dependence with causation.
Recognise independence as a modelling assumption.