Odds

Odds. The word odds is used constantly in probability and statistics as another way of expressing likelihood. Odds relate the number of ways an event CAN occur to the number of ways it CANNOT.

Suppose $a$ is the number of ways an event $A$ can occur, and $b$ is the number of ways it can fail to occur. The odds of $A$ are $a:b$ in favour of $A$, and

Equivalently, odds of $a:b$ in favour of $A$ are the same as odds of $b:a$ against $A$.

Converting the other way. If the probability of an event is already known to be $p$, then the odds in favour of its occurrence are $p$ to $(1-p)$, and the odds against its occurrence are $(1-p)$ to $p$. …