Editing Independence (probability theory) (section)

====Odds====
Stated in terms of [[odds]], two events are independent if and only if the [[odds ratio]] of {{tmath|A}} and {{tmath|B}} is unity (1). Analogously with probability, this is equivalent to the conditional odds being equal to the unconditional odds:
:<math>O(A \mid B) = O(A) \text{ and } O(B \mid A) = O(B),</math>
or to the odds of one event, given the other event, being the same as the odds of the event, given the other event not occurring:
:<math>O(A \mid B) = O(A \mid \neg B) \text{ and } O(B \mid A) = O(B \mid \neg A).</math>
The odds ratio can be defined as
:<math>O(A \mid B) : O(A \mid \neg B),</math>
or symmetrically for odds of {{tmath|B}} given {{tmath|A}}, and thus is 1 if and only if the events are independent.