Chapter 13.3, Problem 24PS

Racetracks quote the approximate odds for each race on a large display board called a tote board.

Here’s what it might say for a particular race:

Horse Number	Odds
1	18 to 1
2	3 to 2
3	2 to 1
4	7 to 5
5	1 to 1

What will be the probability of winning for each of these horses? Note: The odds stated are for the horse’s losing. Thus,

$P\left(horse 1 losing\right)=\frac{18}{18+1}=\frac{18}{19}$

So

$P\left(horse 1 winning\right)=1-\frac{18}{19}=\frac{1}{19}$