The grade appeal process at a university requires that a jury structured by sele
ID: 3160658 • Letter: T
Question
The grade appeal process at a university requires that a jury structured by selecting four individuals randomly from a pool of eight students and six 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? What is the probability of selecting a jury of all students? (Round to five decimal places as needed.) What is the probability of selecting a jury of all faculty? (Round to five decimal places as needed.) What is the probability of selecting a jury of two students and two faculty? (Round to five decimal places as needed.)Explanation / Answer
Given quantities are,
Total Number of students=8
Total number of faculty=6
Total individuals=8+6=14
We know the classical definition of probability is
P(A)=n(A)/n(S)
so first we want to find n(S)=Number of Outcome in sample space.
n(S)=nCr=n combination r
=14C4 (We have Total 14 individuals and want to select 4 individuals)
=1001
n(A)=8C4 (Out of 8 students 4 will be selected)
=70
P(A)=n(A) / n(S)
=70 / 1001
= 0.06993
2.Now we define event B=selecting a jury of all faculty
n(B)=6C4 (Out of 6 faculty 4 will be selected)
=15
P(B)=n(B) / n(S)
=15 / 1001
= 0.014985
3.Now we define event C=selecting a jury of 2 students and 2 faculty
n(C)=8C2*6C2 (Out of 8 students 2 will be selected and out of 6 faculty 2 will be selected)
=28*15
=420
P(C)=n(C) / n(S)
=420 / 1001
= 0.41958
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