For any random events A1,...,AkA_1,...,A_k: Pr[A1∪A2∪...∪Ak]≤Pr[A1]+Pr[A2]+...+Pr[Ak]\mathrm{Pr}[A_1 \cup A_2 \cup ... \cup A_k] \leq \mathrm{Pr}[A_1] + \mathrm{Pr}[A_2] + ... + \mathrm{Pr}[A_k]
(here in Pr[A1∪A2∪...∪Ak]\mathrm{Pr}[A_1 \cup A_2 \cup ... \cup A_k], ∪\cup means “or”)