https://file.aiquickdraw.com/mathbot/file/1729832225426t7x0tdnh.jpg

To solve this problem, we need to calculate the probability of getting at least one '6' when rolling a fair die 5 times.

### Step-by-Step Solution

1. **Calculate the probability of not rolling a '6':**
   - When rolling a die, the probability of not getting a '6' in a single roll is \(\frac{5}{6}\).

2. **Probability of not rolling a '6' in 5 rolls:**
   - Since each roll is independent, the probability of not getting a '6' over 5 rolls is:
     \[
     \left(\frac{5}{6}\right)^5 = \frac{5^5}{6^5} = \frac{3125}{7776}.
     \]

3. **Calculate the probability of getting at least one '6':**
   - To find the probability of getting at least one '6', we use the complement rule:
     \[
     P(\text{at least one '6'}) = 1 - P(\text{no '6' in 5 rolls}).
     \]
     Substituting the value from the previous step:
     \[
     P(\text{at least one '6'}) = 1 - \frac{3125}{7776} = \frac{7776 - 3125}{7776} = \frac{4651}{7776}.
     \]

### Final Answer
The probability of rolling at least one '6' when a die is rolled 5 times is \(\frac{4651}{7776}\).

From the provided options in the image, **Response 3** is the correct choice as it matches \(\frac{4651}{7776}\).

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Would you like further details on this solution or have any other questions? Here are some related questions to deepen your understanding:

1. What is the probability of rolling at least two '6's in 5 rolls?
2. How would the probability change if the die is rolled 6 times instead of 5?
3. What is the probability of rolling a '6' exactly twice in 5 rolls?
4. How is the concept of complementary probability applied in problems like these?
5. What is the expected number of '6's when rolling a die 5 times?

**Tip:** The complement rule is very useful in probability problems, especially when it's easier to calculate the probability of the complementary event.

A die is rolled 5 times. What is the probability of getting at least one '6'?

Learn how to calculate the probability of getting at least one '6' when rolling a die 5 times. This problem covers key probability concepts, including the complement rule. Step-by-step solution provided. Suitable for students in Grades 9-12.

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