To determine the probability of rolling an odd number on a single six-sided die, we go through the following steps:
1. Identify the total number of possible outcomes: A six-sided die has 6 faces, each numbered from 1 to 6.
2. Identify the favorable outcomes: We are interested in the outcomes where the rolled number is odd. The odd numbers between 1 and 6 are 1, 3, and 5. Therefore, there are 3 favorable outcomes.
3. Calculate the probability: The probability of an event occurring is given by 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]
In this scenario, the number of favorable outcomes is 3 (because the odd numbers are 1, 3, and 5), and the total number of possible outcomes is 6 (since there are 6 faces on the die). Therefore, the probability is:
[tex]\[
\text{Probability} = \frac{3}{6} = \frac{1}{2}
\][/tex]
4. Interpret the result: The probability of rolling an odd number on a six-sided die is [tex]\(\frac{1}{2}\)[/tex].
Hence, the correct answer is:
C. [tex]$\frac{1}{2}$[/tex]
