Odds

Odds compare the two complementary probabilities of an event directly, as a ratio of favourable to unfavourable outcomes rather than as a fraction of the total. If a sample space has $n$ equally likely outcomes, $m$ of which favour event $A$, then $P(A)=m/n$ and $P(A')=(n-m)/n$. The odds in favour of $A$ are the ratio of favourable to unfavourable outcomes, $m:(n-m)$, equivalently $P(A):P(A')$. The odds against $A$ are the reverse ratio, unfavourable to favourable, $(n-m):m$, equivalently $P(A'):P(A)$. …