sum rule union bound elementary event when ( holds as an equalityit is often referred to as the sum rule of probability it simply states that if an event can happen in number of different but not simultaneous waysthe probability of that event is the sum of the probabilities of the comprising events if the events are allowed to overlapthen the inequality ( is called the union bound in many applications the sample space is countablethat isohm { in this case the easiest way to specify probability measure is to first assign number pi to each elementary event {ai }with pi and then to define [api for all ohm :ai discrete probability space here the collection of events can be taken to be equal to the collection of all subsets of ohm the triple (ohmhpis called discrete probability space this idea is graphically represented in figure each element ai represented by dotis assigned weight (that isprobabilitypi indicated by the size of the dot the probability of the event is simply the sum of the weights of all the outcomes in figure discrete probability space remark (equilikely principlea special case of discrete probability space occurs when random experiment has finitely many outcomes that are all equally likely in this case the probability measure is given by [aequilikely principle ( where |adenotes the number of outcomes in and |ohmis the total number of outcomes thusthe calculation of probabilities reduces to counting numbers of outcomes in events this is called the equilikely principle random variable | |ohmrandom variables and probability distributions it is often convenient to describe random experiment via "random variables"representing numerical measurements of the experiment random variables are usually denoted by capital letters from the last part of the alphabet from mathematical point of viewa random variable is function from ohm to such that sets of the form { :{ ohm ( bare events (and so can be assigned probability