To determine the probability of rolling a 6 on a fair die, let's go through the problem step by step:
1. Understanding the Total Number of Possible Outcomes:
- A fair die has 6 faces, each numbered from 1 to 6.
- When rolling the die, any one of these 6 faces can land face up.
- Therefore, the total number of possible outcomes is 6.
2. Identifying the Favorable Outcome:
- We are interested in the event where the number 6 lands face up.
- There is only one face on the die that shows the number 6.
3. Calculating the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- So, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Here’s the calculation:
[tex]\[
\text{Probability of rolling a 6} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Since there is only 1 favorable outcome (rolling a 6) and the total number of possible outcomes is 6:
[tex]\[
\text{Probability of rolling a 6} = \frac{1}{6} ≈ 0.16666666666666666
\][/tex]
Therefore, the probability of rolling a 6 on a fair die is approximately 0.1667, which can also be expressed as a fraction 1/6 or a percentage 16.67%.
