The “odds” of an outcome are defined as the ratio of number of events which produce that outcomes to the number of events which do not.
See also Odds ratio.
Q. Define the odds of an event $X$ in terms of $P(X)$
A. odds $= \frac{P(X)}{1 - P(X)}$
Q. What are the odds of rolling a 4 on a six-sided die?
A. 1:5, or 0.2
Q. How to compute the probability of an event from its odds (as a number)?
A. $p = \frac{o}{o + 1}$
Q. Given odds of 0.5, what’s the probability of the event?
A. 1/3
Q. When is the difference between odds and probability largest?
A. When the probability is close to 1.