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To solve this problem, we can use the complementary probability approach. Here's a breakdown of the steps:

### Problem Breakdown:
- **Test setup**: 5 multiple-choice questions, each with 4 answer choices.
- We need to find the probability of getting **at least one question wrong**.

### Complementary Probability Approach:
Instead of directly calculating the probability of getting at least one question wrong, we can first calculate the probability of getting **all the questions correct**, and then subtract this from 1.

1. **Probability of getting one question correct**: Since each question has 4 options and only one is correct, the probability of choosing the correct answer is:
   \[
   P(\text{correct answer}) = \frac{1}{4}.
   \]

2. **Probability of getting all 5 questions correct**: Since the questions are independent, the probability of getting all 5 questions correct is:
   \[
   P(\text{all correct}) = \left( \frac{1}{4} \right)^5 = \frac{1}{1024}.
   \]

3. **Probability of getting at least one question wrong**: This is the complement of getting all the questions correct, so we subtract the probability of getting all correct from 1:
   \[
   P(\text{at least one wrong}) = 1 - \frac{1}{1024} = \frac{1024 - 1}{1024} = \frac{1023}{1024}.
   \]

Thus, the probability of getting at least one question wrong is **\(\frac{1023}{1024}\)**.

Would you like any further details or explanations on this? Here are some related questions for further exploration:

1. What is the probability of getting exactly 1 question wrong?
2. How does the probability change if the number of choices per question increases?
3. What is the expected number of questions a person would get correct by guessing randomly?
4. How would you calculate the probability of getting at least 2 questions wrong?
5. Can the probability of getting at least one question wrong change if the test length is different?

**Tip**: When dealing with probabilities of "at least one" event, consider using the complement rule to simplify your calculation.

On a 5-question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong?

Learn how to calculate the probability of getting at least one question wrong on a 5-question multiple-choice test with 4 answers per question. This problem covers key probability concepts like complementary probability and independent events. Suitable for students in Grades 8-10.

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