Question

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

Answer 1

Jury be structured by selecting six individuals randomly from a pool of eleven students and six faculty

Number of individuals in the jury = 6

Number of students in the pool = 11

Number of faculty in the pool = 6

Total number individuals in the pool = Number of students in the pool + Number of faculty in the pool = 11+6=17

Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool = =12376

17

(a)

Probability of selecting a jury of all​ students

= Number of ways of randomly selecting six students from a pool of 11 students / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

Number of ways of randomly selecting six students from a pool of 11 students = = 462

11

Probability of selecting a jury of all​ students

= Number of ways of randomly selecting six students from a pool of 11 students / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

= 462/12376 = 0.037330317

Probability of selecting a jury of all​ students = 0.037330317

(b)

Probability of selecting a jury of all​ faculty

= Number of ways of randomly selecting six staff from a pool of 6 staff / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

Number of ways of randomly selecting six staff from a pool of 6 staff = =1

6

Probability of selecting a jury of all​ faculty

= Number of ways of randomly selecting six staff from a pool of 6 staff / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

= 1/12376 = 0.000080801551

Probability of selecting a jury of all​ faculty = 0.000080801551

(c)

Probability of selecting a jury of three students and three faculty

= Number of ways of randomly selecting 3 students from a pool of 11 students x Number of ways of randomly selecting 3 staff from a pool of 6 staff / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

Number of ways of randomly selecting 3 students from a pool of 11 students = = 165

11 3

Number of ways of randomly selecting 3 staff from a pool of 6 staff = = 20

3

Number of ways of randomly selecting 3 students from a pool of 11 students x Number of ways of randomly selecting 3 staff from a pool of 6 staff = 165 x 20 = 3300

Probability of selecting a jury of three students and three faculty

= Number of ways of randomly selecting 3 students from a pool of 11 students x Number of ways of randomly selecting 3 staff from a pool of 6 staff / Number of ways of randomly selecting six individuals from a pool of 17 individuals in the pool

= 3300/12376 = 0.26664512

Probability of selecting a jury of three students and three faculty = 0.26664512