or off campus and level in college chart Freshman Sophomore Junior Senior Total Live On Campus 739 4584 1372 2771 9466 Live Off Campus 3321 2099 4285 1296 11001 Total 4060 6683 5657 4067 20467 The following table represents undergraduate students at a local university. One student is chosen at random. Give your answer as a decimal rounded to the ten thousandths (4 places). a. The probability that the student lives off campus or is a junior is

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Certainly! Below is a transcription of the text and an explanation suitable for an educational website.

---

**Transcription:**

1. Yes, since the P(Freshman | Live On Campus) = P(Freshman)
2. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0
3. No, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0
4. Yes, since you can be a freshman that lives on campus
5. No, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ P(Freshman) * P(Live On Campus) = 0.0918
6. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918

e. **Are the events Freshman and Live on Campus independent? Why? Choose a number below**

1. Yes, since P(Freshman | Live On Campus) = P(Freshman)
2. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0
3. No, since P(Freshman Live On Campus) = 0.0361 ≠ 0
4. Yes, since you can be a freshman that lives on campus
5. No, since P(Freshman Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918
6. Yes, since P(Freshman Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918

**Explanation:**

The question asks whether the events "Freshman" and "Live on Campus" are independent. In probabilistic terms, two events A and B are independent if:

\[ P(A \cap B) = P(A) \times P(B) \]

The possible answers present different justifications for the events being independent or not. Key points to consider include:

- **Option 1:** Suggests independence by comparing the conditional probability to the marginal probability.
- **Options 5 and 6:** Address independence with direct reference to the multiplication rule of probabilities and state non-equality,
Transcribed Image Text:Certainly! Below is a transcription of the text and an explanation suitable for an educational website. --- **Transcription:** 1. Yes, since the P(Freshman | Live On Campus) = P(Freshman) 2. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0 3. No, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0 4. Yes, since you can be a freshman that lives on campus 5. No, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ P(Freshman) * P(Live On Campus) = 0.0918 6. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918 e. **Are the events Freshman and Live on Campus independent? Why? Choose a number below** 1. Yes, since P(Freshman | Live On Campus) = P(Freshman) 2. Yes, since P(Freshman ∩ Live On Campus) = 0.0361 ≠ 0 3. No, since P(Freshman Live On Campus) = 0.0361 ≠ 0 4. Yes, since you can be a freshman that lives on campus 5. No, since P(Freshman Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918 6. Yes, since P(Freshman Live On Campus) = 0.0361 ≠ P(Freshman)*P(Live On Campus) = 0.0918 **Explanation:** The question asks whether the events "Freshman" and "Live on Campus" are independent. In probabilistic terms, two events A and B are independent if: \[ P(A \cap B) = P(A) \times P(B) \] The possible answers present different justifications for the events being independent or not. Key points to consider include: - **Option 1:** Suggests independence by comparing the conditional probability to the marginal probability. - **Options 5 and 6:** Address independence with direct reference to the multiplication rule of probabilities and state non-equality,
The image contains data on undergraduate students at a local university, distributed by their living situation (on or off campus) and their academic level (Freshman, Sophomore, Junior, Senior).

### Table: Living on or Off Campus and Level in College

|               | Freshman | Sophomore | Junior | Senior | Total  |
|---------------|----------|-----------|--------|--------|--------|
| **Live On Campus**  | 739      | 4584      | 1372   | 2771   | 9466   |
| **Live Off Campus** | 3321     | 2099      | 4285   | 1296   | 11001  |
| **Total**           | 4060     | 6683      | 5657   | 4067   | 20467  |

### Explanation
- **Live On Campus**: The number of students living on campus is segmented by academic level.
- **Live Off Campus**: The number of students living off campus is similarly segmented.

### Questions
a. **The probability that the student lives off campus or is a junior is**  
   - [To be calculated]

b. **The probability that the student lives on campus and is a senior is**  
   - [To be calculated]

c. **The probability that the student is a freshman given that they live on campus is**  
   - [To be calculated]

d. **Are the events Freshman and Live on Campus mutually exclusive? Why? Choose a number below**  
   - [To be answered] 

Note: The probabilities should be calculated as decimals rounded to four decimal places.
Transcribed Image Text:The image contains data on undergraduate students at a local university, distributed by their living situation (on or off campus) and their academic level (Freshman, Sophomore, Junior, Senior). ### Table: Living on or Off Campus and Level in College | | Freshman | Sophomore | Junior | Senior | Total | |---------------|----------|-----------|--------|--------|--------| | **Live On Campus** | 739 | 4584 | 1372 | 2771 | 9466 | | **Live Off Campus** | 3321 | 2099 | 4285 | 1296 | 11001 | | **Total** | 4060 | 6683 | 5657 | 4067 | 20467 | ### Explanation - **Live On Campus**: The number of students living on campus is segmented by academic level. - **Live Off Campus**: The number of students living off campus is similarly segmented. ### Questions a. **The probability that the student lives off campus or is a junior is** - [To be calculated] b. **The probability that the student lives on campus and is a senior is** - [To be calculated] c. **The probability that the student is a freshman given that they live on campus is** - [To be calculated] d. **Are the events Freshman and Live on Campus mutually exclusive? Why? Choose a number below** - [To be answered] Note: The probabilities should be calculated as decimals rounded to four decimal places.
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