please help with statistics problem ?
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 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?
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First let's get the denominator of the probability by counting the total ways, from 22 individuals of picking *any* 4 of them, without restrictions.
C(22,4) = (22 * 21 * 20 * 19) / (4 * 3 * 2 * 1)
= 7315 ways
Now for each part, you just need to figure the ways of getting the desired outcome and make that the numerator of the probability.
PART A:
From the 13 students, pick 4:C(13,4) = (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
= 715 ways
Answer:
C(13,4) / C(22,4)
= 715/7315
= 13/133
≈ 9.77%
PART B:
From the 9 faculty members, pick 4:
C(9,4) = (9 * 8 * 7 * 5) / (4 * 3 * 2 * 1)
= 105 ways
Answer:
C(9,4) / C(22,4)
= 126/7315
= 18/1045
≈ 1.72%
PART C:
From the 13 students, pick 2.
C(13,2) = (13 * 12) / (2 * 1)
= 78
From the 9 faculty members, pick 2:
C(9,2) = (9 * 8) / (2 * 1)
= 36
78 * 36 = 2808
Answer:
C(13,2) * C(9,2) / C(22,4)
= 2808/7315
≈ 38.4%