Question

an american roulette wheel has 38 slots: 18 red, 18 black, and 2 green. what are the odds for the ball landing in a green slot? what are the odds against the ball landing in a green slot?

Explanation:

Step1: Define odds - for formula

Odds for an event $E$ is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. The number of green slots (favorable outcomes for the ball landing in a green slot) is $n(G)=2$, and the number of non - green slots is $38 - 2=36$.

Step2: Calculate odds for the ball landing in a green slot

The odds for the ball landing in a green slot is $\frac{n(G)}{n(\text{not }G)}=\frac{2}{36}=\frac{1}{18}$, so it is 1 to 18.

Step3: Define odds against formula

Odds against an event $E$ is the ratio of the number of non - favorable outcomes to the number of favorable outcomes.

Step4: Calculate odds against the ball landing in a green slot

The odds against the ball landing in a green slot is $\frac{n(\text{not }G)}{n(G)}=\frac{36}{2}=\frac{18}{1}$, so it is 18 to 1.

Answer:

The odds for the ball landing in a green slot: 1 to 18
The odds against the ball landing in a green slot: 18 to 1