Let's solve the problem step-by-step:
1. Understanding the Problem:
We have a fair, six-sided die, and we need to determine the probability of rolling a 3.
2. Total Outcomes:
Since a six-sided dice has six faces, the total number of possible outcomes when rolling the die is 6.
3. Favorable Outcomes:
Out of these six faces, only one of them is a 3. Therefore, there is only one favorable outcome (rolling a 3).
4. Calculation of Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Hence, the probability \( P \) of rolling a 3 is:
[tex]\[
P(\text{rolling a 3}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6}
\][/tex]
5. Answer:
From the given options, the correct answer is:
[tex]\[
\boxed{\frac{1}{6}}
\][/tex]
So, the probability of a 3 showing on the dice when it is thrown once is [tex]\(\frac{1}{6}\)[/tex], or approximately 0.16666666666666666.
