An inequality concerning the joint probabilities of occurrence of combinations of events. Let E₁, E₂,…, E_m be m events, with E′_j denoting the complementary event to the event E_j , for j=1, 2,…, m. Bonferroni developed various bounds and the inequality that is most often cited isThe most usual context has the event E_j defined as ‘hypothesis test j produces a non-significant result’.