Question

The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of thirteen 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?

Answer 1

Answer with explanation:

Given : Number of individual needed to be selected to form jury = 4

Number of students = 13

Number of faculty members = 6

Total = 13+6=19

Using combinations , the number of combinations of choosing jury of 4 individuals

=
`^(19)C_(4)=(19!)/(4!(19-4)!)\\\\=(19*18*17*16*15!)/(4!15!)=3876`

a) Number of ways of selecting jury of all students

=
`^(13)C_(4)=(13!)/(4!(13-4)!)\\\\=(13*12*11*10*9!)/(4!9!)=715`

The probability of selecting a jury of all​ faculty=
`(715)/(3876)=0.1845`

b) The number of ways of selecting jury of all faculty=
`^(6)C_(4)=(6!)/(4!(6-4)!)=15`

The probability of selecting a jury of all​ faculty=
`(15)/(3876)=0.0039`

c) The number of ways of selecting jury of 2 students and two ​faculty:

`^(13)C_(2)* ^(6)C_2\\\\=(13!)/(2!(13-2)!)*(6!)/(2!(6-2)!)\\\\=1170`

Now, the probability of selecting a jury of six students and two two ​faculty

`(1170)/(3876)=0.3019`