Let's find the probability of rolling either a 3 or a 5 on a fair six-sided die.
1. Understand the Problem:
- We have a fair six-sided die, meaning each side is equally likely to occur.
- The die has faces numbered from 1 to 6.
2. Identify Total Outcomes:
- The total number of possible outcomes when rolling a six-sided die is 6. (This includes rolling a 1, 2, 3, 4, 5, or 6).
3. Identify Favorable Outcomes:
- The favorable outcomes for rolling a 3 or a 5 are 3 and 5.
- There are 2 favorable outcomes (rolling a 3 or rolling a 5).
4. Calculate the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Plugging in the favorable outcomes and total outcomes:
[tex]\[
\text{Probability} = \frac{2}{6}
\][/tex]
5. Simplify the Fraction:
- Simplifying the fraction, we get:
[tex]\[
\frac{2}{6} = \frac{1}{3}
\][/tex]
6. Convert to Decimal:
- Converting the fraction to a decimal, we get approximately:
[tex]\[
\frac{1}{3} \approx 0.333
\][/tex]
7. Check the Answer Choices:
- The options provided are:
- 0.929
- 0.333
- 0.615
- None of the other answers are correct
- 0.28
- Among these, the probability value we calculated matches 0.333.
Therefore, the probability of rolling a 3 or a 5 on a fair six-sided die is 0.333.
