Probability (A-Level)
Conditional, independence, tree diagrams, Venn, addition and multiplication laws.
Builds on GCSE. Key formulae: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A | B) = P(A ∩ B)/P(B); independence ⇔ P(A ∩ B) = P(A)P(B).
Worked examples
P(A ∩ B) = P(A) × P(B|A) = P(B) × P(A|B).
P(A|B) is ‘A given B’. Sample space restricted to B.
Independent events: P(A|B) = P(A).
Frequently asked questions
Mutually exclusive vs independent?
Mutually exclusive can't both happen (so P(A ∩ B) = 0). Independent: knowing one tells you nothing about the other.
Bayes' theorem?
P(A|B) = P(B|A)P(A)/P(B). On the syllabus for some boards.