Past exam of the mathematics course of the University of Cambridge 2004 ia Paper 2 12F Solution Created 2026-09-24 Updated 2026-09-24
Past exam of the mathematics course of the University of Cambridge 2015 ia Paper 2 4F Solution Created 2026-09-24 Updated 2026-10-06
Put , and . Because , the conditional probability inequality is equivalent to . But that same inequality gives , or . Thus positive association of two events is symmetric.
For the complement of an event, , andTherefore strictly repels ; equivalently . Both directions are stated because the wording switches the grammatical roles of attraction and repulsion. The substantive conclusion is the same: the conditional probabilities involving the complement are strictly smaller than their unconditional counterparts.