Question

Find the odds for and the odds against the event rolling a fair die and getting a 2, a 4, a 6, or a 3.

The odds for the event are ___ to ___
The odds against the event are ____ to _____

Answer 1

The odds against it is 2 to 6
The odds for it is 4 to 6

Answer 2

The odds for the event are 2 to 1

The odds against the event are 1 to 2.

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}}`

`\text{Odds in favor}=(4)/(2)`

`\text{Odds in favor}=(2)/(1)`

Odds against for given event is

`\text{Odds against}=\frac{\text{Number of unfavorable outcomes}}{\text{ Number of favorable outcomes}}`

`\text{Odds against}=(2)/(4)`

`\text{Odds against}=(1)/(2)`

The odds for the event are 2 to 1

The odds against the event are 1 to 2.