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The question asks: "A fair die is rolled six times. What is the probability that it comes up 5 at least once?" The goal is to compute the probability that a 5 appears at least once during six rolls of a die.

We can solve this using the complement rule.

### Step-by-step solution:

1. **Complement Rule**: 
   The probability of at least one success (rolling a 5) is 1 minus the probability of no success (never rolling a 5).

2. **Probability of not rolling a 5 in one roll**:
   A fair die has 6 faces, so the probability of *not* rolling a 5 in a single roll is \( \frac{5}{6} \) (since there are 5 other numbers on the die).

3. **Probability of not rolling a 5 in six rolls**:
   Since the rolls are independent, the probability of not rolling a 5 for six consecutive rolls is \( \left(\frac{5}{6}\right)^6 \).

4. **Complement Probability**:
   The probability of rolling at least one 5 is:
   \[
   P(\text{at least one 5}) = 1 - P(\text{no 5s}) = 1 - \left(\frac{5}{6}\right)^6
   \]
   
5. **Calculation**:
   \[
   P(\text{at least one 5}) = 1 - \left(\frac{5}{6}\right)^6 \approx 1 - 0.3349 = 0.6651
   \]
   
So, the probability that a 5 appears at least once is approximately **0.6651**.

Would you like further details, or do you have any questions?

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Here are 5 related questions:
1. What is the probability of rolling a 5 exactly once in six rolls?
2. How would the probability change if the die is rolled 10 times?
3. What is the probability of getting a 5 in every roll of six trials?
4. How does this probability change if the die is not fair (biased)?
5. What is the expected number of times a 5 will appear in six rolls?

**Tip**: The complement rule is very useful when calculating probabilities involving "at least" scenarios because it simplifies the process of dealing with multiple possibilities.

A fair die is rolled six times. What is the probability that it comes up 5 at least once? Write your answer as a fraction or decimal, rounded to four decimal places.

Find out the probability of rolling a 5 at least once in six rolls of a fair die. The solution uses the complement rule and includes key concepts like independent events and basic probability calculations. Suitable for students in Grades 8-10.

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