Question

find the odds for rolling a 6 - sided die and getting a 3. find the odds against rolling a 6 - sided die and getting a 3. simplify your answers.

Explanation:

Step1: Define favorable and non - favorable outcomes

When rolling a 6 - sided die, the total number of possible outcomes is $n = 6$. The event of getting a 3 has 1 favorable outcome ($n_f=1$) and $n_{nf}=6 - 1=5$ non - favorable outcomes.

Step2: Calculate odds for getting a 3

The odds for an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. So, odds for getting a 3 is $\frac{n_f}{n_{nf}}=\frac{1}{5}$, or 1 to 5.

Step3: Calculate odds against getting a 3

The odds against an event is the ratio of the number of non - favorable outcomes to the number of favorable outcomes. So, odds against getting a 3 is $\frac{n_{nf}}{n_f}=\frac{5}{1}$, or 5 to 1.

Answer:

1. Odds for rolling a 6 - sided die and getting a 3: 1 to 5
2. Odds against rolling a 6 - sided die and getting a 3: 5 to 1