Find the odds against Nicole winning a ring? Find the odds in favor of Nicole winning a ring?

We will have the following:
The odds of Nicole winning a ring are:
[tex]P=\frac{3}{9}\Rightarrow P=\frac{1}{3}[/tex]So, the odds of Nicole winning a ring are 1:3.
And by transitivity, the odds of Nicole not winning a ring are 2:3.