Boole's inequality [SEP] named after
Boole's inequality
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Boole's inequality is named after George Boole.
Formally, for a countable set of events "A", "A", "A", ..., we have
In measure-theoretic terms, Boole's inequality follows from
vase should have infinitely many balls, that has warranted this problem to be named the Ross–Littlewood paradox.
Ross's probabilistic version of the problem extended the removal method to the case where whenever a ball is to be withdrawn that ball is uniformly randomly selected from among those present in the vase at that time. He showed in this case that the probability that any particular ball remained in the vase at noon was 0 and therefore, by using Boole's inequality and taking a countable sum over the balls, that the