basic properties with respect to events defined from pr( pr( <pr( < for any if , and ab othen pr(aubpr( +pr(btwo events and are independent if pr(abpr( )*pr(ba collection of events { is mutually independent if pr( ik pr( pr( ***pr( ik for any subset { , , ik the conditional probability that an event occursgiven an event bis denoted as pr( | )and is defined as the ratio pr(ab)/pr( )assuming that pr( an elegant way for dealing with events is in terms of random variables intuitivelyrandom variables are variables whose values depend upon the outcome of some experiment formallya random variable is function that maps outcomes from some sample space to real numbers an indicator random variable is random variable that maps outcomes to the set { , often in data structure and algorithm analysis we use random variable to characterize the running time of randomized algorithm in this casethe sample space is defined by all possible outcomes of the random sources used in the algorithm we are most interested in the typicalaverageor "expectedvalue of such random variable the expected value of random variable is defined as where the summation is defined over the range of (which in this case is assumed to be discreteproposition (the linearity of expectation)let and be two random variables and let be number then