probability stats

Question

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 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 two students and two ​faculty?

Answer 1

a) For the first pick, the probability of selecting a student is 9/18 (or 1/2). For the second pick, the probability of selecting a student is 8/17 (since you already selected one student). For the third pick, the probability of selecting a student is 7/16. And for the fourth pick, the probability of selecting a student is 6/15 (or 2/5).

So the probability of selecting 4 students is (1/2)•(8/17)•(7/16)•(2/5) = 7/170

b) Perform the same math as a)

c) There are 6 ways to get two students and two faculty:

SSFF with a probability = (1/2)•(8/17)•(9/16)•(8/15) = 6/85

SFSF with a probability = (1/2)•(9/17)•(1/2)•(8/15) = 6/85

SFFS with a probability = (1/2)•(9/17)•(1/2)•(8/15) = 6/85

FSSF with a probability = (1/2)•(9/17)•(1/2)•(8/15) = 6/85

FSFS with a probability = (1/2)•(8/17)•(1/2)•(8/15) = 6/85

FFSS with a probability = (1/2)•(8/17)•(9/16)•(8/15) = 6/85

Add these together to get 36/85