Answer:
The odds for the event are 2 to 1
The odds against the event are 1 to 2.
Step-by-step explanation:
Let A be the event of rolling a fair die and getting a 2, a 4, a 6, or a 3.
Total number of outcomes = 6
Favorable outcomes = 4
Unfavorable outcomes = 6 - 4 = 2
Odds in favor for given event is
![\text{Odds in favor}=\frac{\text{ Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20in%20favor%7D%3D%5Cfrac%7B%5Ctext%7B%20Number%20of%20favorable%20outcomes%7D%7D%7B%5Ctext%7BNumber%20of%20unfavorable%20outcomes%7D%7D)
![\text{Odds in favor}=\frac{4}{2}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20in%20favor%7D%3D%5Cfrac%7B4%7D%7B2%7D)
![\text{Odds in favor}=\frac{2}{1}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20in%20favor%7D%3D%5Cfrac%7B2%7D%7B1%7D)
Odds against for given event is
![\text{Odds against}=\frac{\text{Number of unfavorable outcomes}}{\text{ Number of favorable outcomes}}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20against%7D%3D%5Cfrac%7B%5Ctext%7BNumber%20of%20unfavorable%20outcomes%7D%7D%7B%5Ctext%7B%20Number%20of%20favorable%20outcomes%7D%7D)
![\text{Odds against}=\frac{2}{4}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20against%7D%3D%5Cfrac%7B2%7D%7B4%7D)
![\text{Odds against}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Ctext%7BOdds%20against%7D%3D%5Cfrac%7B1%7D%7B2%7D)
The odds for the event are 2 to 1
The odds against the event are 1 to 2.