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To determine which quiz Joe is more likely to get 100% correct by guessing, we need to calculate the probabilities for both quizzes based on the provided information:

### Science Quiz:
- 7 true-false questions.
- Probability of guessing each question correctly = \(0.5\).
- Probability of getting all 7 questions correct by guessing = \( (0.5)^7 \).

### English Quiz:
- 3 multiple-choice questions.
- Probability of guessing each question correctly = \(0.25\) (since each multiple-choice question has 4 options).
- Probability of getting all 3 questions correct by guessing = \( (0.25)^3 \).

Let me calculate these probabilities.The probabilities of getting all questions correct by guessing are:

- **Science Quiz**: \(0.0078125\) or approximately \(0.008\).
- **English Quiz**: \(0.015625\) or approximately \(0.016\).

Since the probability of getting all questions correct in the **English quiz** (0.016) is higher than in the **Science quiz** (0.008), Joe should study for the **Science quiz**, where he is more likely to do worse by guessing.

This corresponds to **option A**: "Science, because the probability of getting all questions correct is 0.008, which is lower than for English (0.016)."

Would you like further details or clarifications?

Here are 5 related questions to deepen understanding:
1. How would the probabilities change if the number of questions increased for both quizzes?
2. What if the English quiz had more than 4 options per question?
3. How would the probability change for the Science quiz if there were more than two answer choices per question?
4. How does the concept of independent events apply to these probability calculations?
5. Can Joe improve his chances by eliminating some incorrect answers before guessing?

**Tip**: When guessing, the probability of getting all questions right decreases exponentially with the number of questions!

Joe has to take two quizzes tomorrow. He has only enough time to study for one of them. The Science quiz has 7 true-or-false questions, and the English quiz has 3 multiple-choice questions. Joe calculates the probability that he will get each question correct by guessing.

Learn how to calculate the probability of getting all questions correct by guessing in both a true-or-false quiz and a multiple-choice quiz. This problem explores key probability concepts, suitable for students in Grades 7-9.

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