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The grade appeal process at a university requires that a jury be structured by selecting four...

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?

Expert Solution

Number of students in the pool = 13

Number of faculty in the pool = 9

Total number students + faculty in the pool = 13+9 =22

Number of individuals in the jury = 4

Number of possible juries if there were no restrictions= Number of ways of selecting 4-individuals for jury without any restriction from the pool of 22 = =7315

(a) Probability of selecting a jury of all students

= Number of possible juries with students only / Number of possible juries if there were no restrictions

Number of possible juries with students only = Number of ways of selecting 4- individual for jury from a pool of 13 students == 715

Probability of selecting a jury of all students

= Number of possible juries with students only / Number of possible juries if there were no restrictions

= 715/7315 = 0.097744361

Probability of selecting a jury of all students = 0.097744361

(b) Probability of selecting a jury of all faculty

= Number of possible juries with faculty only / Number of possible juries if there were no restrictions

Number of possible juries with faculty only = Number of ways of selecting 4-individual jury from a pool of 9 faculty == 126

Probability of selecting a jury of all faculty

= Number of possible juries with faculty only / Number of possible juries if there were no restrictions

= 126/7315 = 0.01722488

Probability of selecting a jury of all faculty = 0.01722488

(c) probability of selecting a jury of two students and two faculty

= Number of possible juries with two students and two faculty only / Number of possible juries if there were no restrictions

Number of ways of selecting 2 students from a pool of 13 students and 2-faculty from a pool of 9 faculty =

Probability of selecting a jury of two students and two faculty

= Number of possible juries with two students and two faculty only / Number of possible juries if there were no restrictions

= 2808 / 7315 = 0.383868763

Probability of selecting a jury of two students and two faculty = 0.383868763

milcah answered 1 year ago

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