d. Are the events Freshman and Live on Campus mutually exclusive? Why? Choose a number below 1. Yes, since the P(Freshman Live On Campus) = P(Freshman) 2. Yes, since P(Freshman N Live On Campus) = 0.0361 * 0 3. No, since P(Freshman N Live On Campus) = 0.0361 * 0 %3D %3D %3D 4. Yes, since you can be a freshman that lives on campus 5. No, since P(Freshman N Live On Campus) = 0.0361 * P(Freshman)*P(Live On %3D Campus) = 0.0918 %3D 6. Yes, since P(Freshman N Live On Campus) = 0.0361 * P(Freshman)*P(Live On Campus) = 0.0918 %3D e. Are the events Freshman and Live on Campus independent? Why? Choose a number below 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 %3D

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I only need help with "D" and "E" never seen a problem with this type of ending. Thank you!!
### Probability Concepts: Mutually Exclusive and Independent Events

#### Question d: Are the events Freshman and Live on Campus mutually exclusive? 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

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

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

### Explanation of Concepts

- **Mutually Exclusive Events:** Two events are mutually exclusive if they cannot occur simultaneously. In probability terms, if P(A ∩ B) = 0, events A and B are mutually exclusive.

- **Independent Events:** Two events are independent if the occurrence of one event does not affect the probability of the other. Mathematically, two events A and B are independent if P(A ∩ B) = P(A) * P(B). 

The questions above prompt students
Transcribed Image Text:### Probability Concepts: Mutually Exclusive and Independent Events #### Question d: Are the events Freshman and Live on Campus mutually exclusive? 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 #### Question e: Are the events Freshman and Live on Campus independent? Why? Choose a number below. 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 ### Explanation of Concepts - **Mutually Exclusive Events:** Two events are mutually exclusive if they cannot occur simultaneously. In probability terms, if P(A ∩ B) = 0, events A and B are mutually exclusive. - **Independent Events:** Two events are independent if the occurrence of one event does not affect the probability of the other. Mathematically, two events A and B are independent if P(A ∩ B) = P(A) * P(B). The questions above prompt students
### Living on 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  |

#### Explanation

This table shows the distribution of students living on and off campus across different academic levels: Freshman, Sophomore, Junior, and Senior. The totals at the bottom represent the sum of students in each column.

#### Probability Questions

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: [Space for Answer]

b. The probability that the student lives on campus **and** is a senior is: [Space for Answer]
Transcribed Image Text:### Living on 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 | #### Explanation This table shows the distribution of students living on and off campus across different academic levels: Freshman, Sophomore, Junior, and Senior. The totals at the bottom represent the sum of students in each column. #### Probability Questions 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: [Space for Answer] b. The probability that the student lives on campus **and** is a senior is: [Space for Answer]
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