What is the probability of rolling a 3 on a fair six-sided die?

The probability of rolling a 3 on a fair six-sided die is determined by recognizing how many outcomes are favorable compared to the total number of possible outcomes. A fair six-sided die has six faces, numbered from 1 to 6.

When analyzing the situation, the only favorable outcome for rolling a 3 is if the die lands on the face showing 3, which is just one specific outcome. Therefore, the number of favorable outcomes is 1.

Next, to find the total number of outcomes, we count all the faces of the die, which amounts to 6.

The probability can be calculated using the formula:

[

\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6}

]

This fraction captures the likelihood of rolling a 3 compared to all the possible outcomes on a die, making the answer ( \frac{1}{6} ). In this scenario, rolling other numbers (1, 2, 4, 5, and 6) does not contribute to the successful event of rolling a 3, emphasizing that only the specific face matters for this probability calculation.