Question

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of ten students and ten 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 three students and two faculty?

Answer 1

jury be structured by selecting five individuals randomly from a pool of ten students and ten faculty.

P[ Selecting a student ] = 5/10 = 0.5

P[ Selecting a faculty ] = 5/10 = 0.5

(a) What is the probability of selecting a jury of all​ students?

P[ selecting a jury of all​ students ] = P[ Selecting a student ]^5 = 0.5*0.5*0.5*0.5*0.5 = 0.03125

(b) What is the probability of selecting a jury of all​ faculty?

P[ selecting a jury of all​ faculty ] = P[ Selecting a faculty ]^5 = 0.5*0.5*0.5*0.5*0.5 = 0.03125

(c) What is the probability of selecting a jury of three students and two faculty?

P[ selecting a jury of three students and two faculty ] = Arrangement of 3 students and 2 jury * 0.5^3*0.5^2

Arrangement of 3 students and 2 jury   

P[ selecting a jury of three students and two faculty ] =10*0.5^5

P[ selecting a jury of three students and two faculty ] = 0.3125