Question

The grade appeal process at a university requires that a jury be structured by selecting seven individuals randomly from a pool of eleven students and nine 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 three students and four faculty (Round to five decimal places as needed)

Answer 1

The probability of selecting a jury of all students is 0.00426, the probability of selecting a jury of all faculty is 0.00046, and the probability of selecting a jury of 3 students and 4 faculty members is 0.26777.

Step-by-step explanation:

To calculate the probabilities, we need to find the total number of possible juries and the number of favorable outcomes for each scenario.

1. To find the probability of selecting a jury of all students, we need to select 7 students from the pool of 11. The number of ways to select 7 students from 11 is C(11, 7) = 330, since we are choosing a combination of students. The total number of possible juries is C(20, 7) = 77520, since we are choosing a combination of 7 individuals from a pool of 20. Therefore, the probability of selecting a jury of all students is 330/77520 = 0.00426 (rounded to five decimal places).
2. To find the probability of selecting a jury of all faculty, we need to select 7 faculty members from the pool of 9. The number of ways to select 7 faculty members from 9 is C(9, 7) = 36. The total number of possible juries is still 77520, since we are choosing a combination of 7 individuals from a pool of 20. Therefore, the probability of selecting a jury of all faculty is 36/77520 = 0.00046 (rounded to five decimal places).
3. To find the probability of selecting a jury of 3 students and 4 faculty members, we need to select 3 students from the pool of 11 and 4 faculty members from the pool of 9. The number of ways to select 3 students from 11 is C(11, 3) = 165 and the number of ways to select 4 faculty members from 9 is C(9, 4) = 126. The total number of possible juries is still 77520. Therefore, the probability of selecting a jury of 3 students and 4 faculty members is (165 * 126)/77520 = 0.26777 (rounded to five decimal places).