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To solve this problem, we need to calculate the probability of getting at least one question wrong on a 9-question multiple-choice test where each question has 4 possible answers.

### Step-by-Step Solution

1. **Probability of Getting One Question Right:**
   Each question has 4 choices, and only 1 is correct. So, the probability of selecting the correct answer for any given question is:
   \[
   \frac{1}{4}
   \]

2. **Probability of Getting All Questions Right:**
   Since there are 9 questions and each question must be answered correctly to get them all right, the probability of getting all 9 questions correct is:
   \[
   \left(\frac{1}{4}\right)^9 = \frac{1}{4^9}
   \]

3. **Probability of Getting At Least One Question Wrong:**
   The probability of getting at least one question wrong is the complement of getting all questions right. So, we calculate this as:
   \[
   1 - \frac{1}{4^9}
   \]

4. **Calculating \(4^9\):**
   \(4^9 = 262144\), so:
   \[
   1 - \frac{1}{262144} = \frac{262144 - 1}{262144} = \frac{262143}{262144}
   \]

### Final Answer
The probability of getting at least one question wrong is:
\[
\frac{262143}{262144}
\]

Would you like further details on this solution or have any questions?

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Here are some related questions for further exploration:

1. What would the probability be of getting exactly one question wrong on this test?
2. How would the probability change if each question had only 3 answers instead of 4?
3. What is the probability of getting at least two questions wrong on a similar test?
4. How does the probability change if the test has more questions, say 12 instead of 9?
5. How can we generalize this problem for a test with \( n \) questions and \( m \) answer choices per question?

**Tip:** In probability problems, using complements (like calculating the probability of "at least one wrong" by finding "all correct" first) often simplifies the calculations.

On a 9-question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong?

Calculate the probability of getting at least one question wrong on a 9-question multiple-choice test where each question has 4 options. This problem uses the concept of complementary probability and is suitable for high school students.

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