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 red slot? to what are the odds against the ball landing in a red slot? to simplify your answers.

Explanation:

Step1: Define odds - for formula

Odds - for an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes.
The number of red slots (favorable for ball landing in red) is $n(R)=18$, and the number of non - red slots is $38 - 18=20$.

Step2: Calculate odds for ball landing in red

The odds for the ball landing in a red slot is $\frac{n(R)}{n(\text{not }R)}=\frac{18}{20}=\frac{9}{10}$, so it is 9 to 10.

Step3: Define odds - against formula

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

Step4: Calculate odds against ball landing in red

The odds against the ball landing in a red slot is $\frac{n(\text{not }R)}{n(R)}=\frac{20}{18}=\frac{10}{9}$, so it is 10 to 9.

Answer:

The odds for the ball landing in a red slot: 9 to 10
The odds against the ball landing in a red slot: 10 to 9