What does it mean by "odds that an event will occur is $2$ to $3$"? > In a swimming race, the odds that $A$ will win are 2 to 3 and the odds that $B$ will win are 1 to 4 Find the probability $p$ and the odds that $A$ or $B$ wins the race. What does it mean by odds that an event will occur is $2$ to $3$?

The _odds_ are $2:3$ when the _probability_ is $2/(2+3) = 2/5$.

**Edit** in response to comment.

Indeed odds are just ratios. $2:3$ is the same as $4:6$. I don't know why they came to be written that way, but I'm glad they are. If you think of them as fractions it's all too easy to confuse them with probabilities. Of course they can't be, since odds of $3:2$ make perfect sense but a probability of $3/2$ doesn't.

Odds are the usual way to express stakes in a bet. If the probability of an event is $2/5$ (as in your example) then it would be fair to stake $\$3$ against $\$2$ in a bet. You and your opponent each put the stake ($\$2$ or $\$3$) into the pot; the winner takes it all.