The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of nine students and thirteen faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of two students and two faculty? (a) What is the probability of selecting a jury of all students? (Round to five decimal places as needed.) (b) What is the probability of selecting a jury of all faculty? (Round to five decimal places as needed.) (c) What is the probability of selecting a jury of two students and two faculty? (Round to five decimal places as needed.)

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**Title: Understanding Probability in Jury Selection for Grade Appeals**

**Introduction:**
The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of nine students and thirteen faculty. This exercise will help in understanding the probability calculations needed to answer specific scenarios regarding the jury selection process.

**Questions and Probabilities:**

1. **What is the probability of selecting a jury of all students?**

   - [ ] (Round to five decimal places as needed.)
   
2. **What is the probability of selecting a jury of all faculty?**

   - [ ] (Round to five decimal places as needed.)
   
3. **What is the probability of selecting a jury of two students and two faculty?**

   - [ ] (Round to five decimal places as needed.)

**Notes:**

- Ensure to use combinations (nCr) to calculate the probability accurately.
- For each scenario, you need to consider the total possible combinations of selecting four individuals out of twenty-two (students + faculty).

Let’s break down each part:

**(a) Probability of Selecting a Jury of All Students:**
- Calculate the combination of selecting 4 students out of 9.
- Divide by the total combination of selecting 4 members out of 22.

**(b) Probability of Selecting a Jury of All Faculty:**
- Calculate the combination of selecting 4 faculty members out of 13.
- Divide by the total combination of selecting 4 members out of 22.

**(c) Probability of Selecting a Jury of Two Students and Two Faculty:**
- Calculate the combination of selecting 2 students out of 9.
- Calculate the combination of selecting 2 faculty out of 13.
- Multiply these two results and divide by the total combination of selecting 4 members out of 22.

Through these steps, you will get the required probabilities, which can then be rounded to five decimal places as specified.
Transcribed Image Text:**Title: Understanding Probability in Jury Selection for Grade Appeals** **Introduction:** The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of nine students and thirteen faculty. This exercise will help in understanding the probability calculations needed to answer specific scenarios regarding the jury selection process. **Questions and Probabilities:** 1. **What is the probability of selecting a jury of all students?** - [ ] (Round to five decimal places as needed.) 2. **What is the probability of selecting a jury of all faculty?** - [ ] (Round to five decimal places as needed.) 3. **What is the probability of selecting a jury of two students and two faculty?** - [ ] (Round to five decimal places as needed.) **Notes:** - Ensure to use combinations (nCr) to calculate the probability accurately. - For each scenario, you need to consider the total possible combinations of selecting four individuals out of twenty-two (students + faculty). Let’s break down each part: **(a) Probability of Selecting a Jury of All Students:** - Calculate the combination of selecting 4 students out of 9. - Divide by the total combination of selecting 4 members out of 22. **(b) Probability of Selecting a Jury of All Faculty:** - Calculate the combination of selecting 4 faculty members out of 13. - Divide by the total combination of selecting 4 members out of 22. **(c) Probability of Selecting a Jury of Two Students and Two Faculty:** - Calculate the combination of selecting 2 students out of 9. - Calculate the combination of selecting 2 faculty out of 13. - Multiply these two results and divide by the total combination of selecting 4 members out of 22. Through these steps, you will get the required probabilities, which can then be rounded to five decimal places as specified.
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