The following table represents undergraduate students at a local university. One student is chosen at random. Junior Senior Total 1886 1804 8750 1413 3815 9514 3299 5619 18264 Live On Campus Live Off Campus Total Freshman Sophomore 2001 2483 4484 3059 1803 4862 a) Find the probability that the student lives off campus or is a junior.
The following table represents undergraduate students at a local university. One student is chosen at random. Junior Senior Total 1886 1804 8750 1413 3815 9514 3299 5619 18264 Live On Campus Live Off Campus Total Freshman Sophomore 2001 2483 4484 3059 1803 4862 a) Find the probability that the student lives off campus or is a junior.
MATLAB: An Introduction with Applications
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![The following table represents undergraduate students at a local university. One student is chosen at random.
| | Freshman | Sophomore | Junior | Senior | Total |
|-------------------|----------|-----------|--------|--------|--------|
| **Live On Campus** | 2001 | 3059 | 1886 | 1804 | 8750 |
| **Live Off Campus** | 2483 | 1803 | 1413 | 3815 | 9514 |
| **Total** | 4484 | 4862 | 3299 | 5619 | 18264 |
**a)** Find the probability that the student lives off campus *or* is a junior.
[Input box]
**b)** Find the probability that the student lives on campus *and* is a senior.
[Input box]
**c)** Find the probability that the student is a freshman given that they live on campus.
[Input box]
[Submit Question Button]
### Explanation of Probabilities:
- **a)** Probability of living off campus *or* being a junior: Calculate using the formula for the probability of the union of two events, which requires adding the probabilities of each event and subtracting the probability of their intersection.
- **b)** Probability of living on campus *and* being a senior: Determine by dividing the number of students who are both on-campus seniors by the total number of students.
- **c)** Conditional probability of being a freshman given living on campus: Use the formula for conditional probability which is the probability of the intersection of the two events divided by the probability of the condition event occurring.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F998c0d1a-ff65-42b1-8215-acf4aa1ab8d8%2Fcbe9cd8d-7d53-46bf-8331-7c792d71c17d%2Fn0giprj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following table represents undergraduate students at a local university. One student is chosen at random.
| | Freshman | Sophomore | Junior | Senior | Total |
|-------------------|----------|-----------|--------|--------|--------|
| **Live On Campus** | 2001 | 3059 | 1886 | 1804 | 8750 |
| **Live Off Campus** | 2483 | 1803 | 1413 | 3815 | 9514 |
| **Total** | 4484 | 4862 | 3299 | 5619 | 18264 |
**a)** Find the probability that the student lives off campus *or* is a junior.
[Input box]
**b)** Find the probability that the student lives on campus *and* is a senior.
[Input box]
**c)** Find the probability that the student is a freshman given that they live on campus.
[Input box]
[Submit Question Button]
### Explanation of Probabilities:
- **a)** Probability of living off campus *or* being a junior: Calculate using the formula for the probability of the union of two events, which requires adding the probabilities of each event and subtracting the probability of their intersection.
- **b)** Probability of living on campus *and* being a senior: Determine by dividing the number of students who are both on-campus seniors by the total number of students.
- **c)** Conditional probability of being a freshman given living on campus: Use the formula for conditional probability which is the probability of the intersection of the two events divided by the probability of the condition event occurring.
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