Independence (probability theory)
Conditional dependence
In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. For example, if and are two events that individually increase the probability of a third event and do not directly affect each other, then initially (when it has not been observed whether or not the event occurs) ( are independent). But suppose that now is observed to occur. If event occurs then the probability of occurrence of the event will decrease because its positive relation to is less necessary as an explanation for the occurrence of (similarly, event occurring will decrease the probability of occurrence of ). Hence, now the two events and are conditionally negatively dependent on each other because the probability of occurrence of each is negatively dependent on whether the other occurs. We have Conditional dependence of A and B given C is the logical negation of conditional independence . In conditional independence two events (which may be dependent or not) become independent given the occurrence of a third event. (Wikipedia).
