The problem asks to find the probability $P(3)$ when a fair die is rolled. The sample space for a fair die roll is $\{1, 2, 3, 4, 5, 6\}$, and all outcomes are equally likely.

To calculate the probability of rolling a 3, we use the formula for probability:

$P(3) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}.$

In this case:

• The favorable outcome is rolling a 3, which occurs only once.
• The total number of outcomes is 6 (since the die has 6 faces).

Thus:

$P(3) = \frac{1}{6}.$

So, the exact probability $P(3)$ is $\frac{1}{6}$.

Would you like more details on this? Here are five related questions for deeper understanding:

1. What is the probability of rolling an even number on a fair die?
2. How does the probability change if the die is biased towards certain numbers?
3. What is the probability of rolling a number less than 5?
4. How would you calculate the probability of rolling a number greater than 4?
5. How would the sample space change if we were rolling two dice instead of one?

Tip: When working with probability, always remember that the total outcomes in the sample space should account for every possible scenario.