A lower bound on the probability P(Ai ∪ ⋯ ∪ Am) is presented, in terms of the P(Ai)'s and P(Ai ∩ Aj)'s only. A comparison is made to a similar inequality due to Dawson and Sankoff (1967).
De Caen, D. (1997). A lower bound on the probability of a union. Discrete Mathematics, 169(1–3), 217–220. https://doi.org/10.1016/S0012-365X(96)00107-0