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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.

Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6}, and all the outcomes are equally likely. Find P(3). Express your answer in exact form.

Learn how to calculate the exact probability of rolling a 3 when a fair die is rolled. This problem covers key probability concepts, including sample space and equally likely outcomes. Suitable for students in Grades 6-8.

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