Question

The grade appeal process requires that a jury be structured selecing eight individuals randomly from a pool of 12 students and 12 falculty.Whai is the probability of selecting all students

Answer 1

0.07% probability of selecting all students

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the jury is selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

What is the probability of selecting all students?

Desired outcomes:

8 students from a set of 12. So

`D = C_(12,8) = (12!)/(8!4!) = 495`

Total outcomes:

8 people from a set of 12+12 = 24. So

`T = C_(24,8) = (24!)/(8!16!) = 735471`

Probability:

`p = (D)/(T) = (495)/(735471) = 0.0007`

0.07% probability of selecting all students