The probability of rolling a 3 on a fair six-sided die is given by the fraction $\frac{1}{6}$.

When you roll a fair six-sided die, each of the six faces has an equal likelihood of landing face up. This characteristic indicates that the die is unbiased, meaning no number is more likely to appear than any other. The numbers represented on a standard die are $1$, $2$, $3$, $4$, $5$, and $6$. Since there is only one face showing the number $3$, and there are a total of six possible outcomes, the probability of rolling a $3$ can be determined by calculating the ratio of the number of favorable outcomes to the total number of possible outcomes.

To compute this probability, you can use the following formula:

In this scenario, the number of favorable outcomes (rolling a $3$) is $1$, while the total number of possible outcomes (the numbers $1$ through $6$) is $6$. Therefore, the probability is calculated as follows:

This fraction can also be represented as a decimal, approximately $0.1667$, or as a percentage, roughly $16.67\%$. However, in most GCSE Maths problems, it is generally advisable to express the answer as a fraction, which is both acceptable and often preferred.

Grasping this fundamental concept of probability is crucial, as it serves as the foundation for more advanced topics in statistics and probability theory.