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The odds of an event is the ratio of the probability that the event will happen (p) to the probability that it will not happen (1-p).

The odds of an event is the quotient of the probability of the event divided by the probability the event will not occur: $$ \text{odds}=\frac{\text{probability}}{1-\text{probability}} $$ The odds of a fair coin are $1=\frac{.50}{.50}$. If a probability is $<50\%$, the odds will be $<1$, and if $>50\%$, then $>1$. Odds can range from $(0,~\infty)$.

In some ways, it can be more useful to work with odds than probabilities, even though people often feel the latter are more intuitive. Specifically, odds and odds ratios are very helpful in logistic regression.

Outside of a statistical context, people are familiar with odds being presented in a manner such as $3:2$. This format is called 'Las Vegas' odds (actually, the 'odds' presented in a casino are not the actual odds of winning / losing, but rather the payouts associated with winning or losing). In a statistical context, however, we divide through and present a single number (e.g., $1.5$).