let be a countable set and let be pairwise disjoint sets with . then, for any with and any ,
let be a partition of the sample space, and let be any set. then, for each ,
in simpler terms,
the probability of A occuring, knowing that B has occured is
two events are independent if knowing one event occurred doesn't change the probability of the other event. otherwise they are both dependent on one another i.e. two events, A and B, are independent if: