Many of the statistical methods for the analysis of binary outcome variables are based on the odds of an event, rather than on its probability.
The Odds of event A are defined as the probability that A does happen divided by the probability that it does not happen:
Odds (A= prob (A happens) / prob (A does not happen) = prob (A) / 1- prob (A)
Since 1- prob (A) is the probability that A does not happen. By manipulating this equation, it is also possible to express the probability in terms of the odds:
Prob (A) = Odds (A) / 1+ Odds (A)
Thus it is possible to derive the odds from the probability and vice versa.
It can be seen that while probabilities must lie between o and 1, odds can take any value between o and infinity .
Thus the odds are always bigger than the probability (since 1- prob (A) is less than one).