There are five school officials at PCC who might be able to

There are five school officials at PCC who might be able to serve on a committee to investigate improving success in math courses: The Dean of Instruction (DOI), the Dean of Students (DOS), the Vice President of Student and Academic Affairs (VPSAA), the Division Dean overseeing mathematics (DD), and the Campus President (CP). Consider all possible groups of size 3 that can be obtained from this population of five officials. (Note: there are 10 possible samples!)


(a) What is the probability that the DOI and the CP are included in the sample?

(b) What is the probability that the DOI and the DOS are included in the sample?

Solution

No of Samples in which DOI and the CP are included = {DOI, CP, DOS} , {DOI, CP, VPSAA} , (DOI, CP, CA}

probability that the DOI and the CP are included in the sample = 3/10 = 0.3

Similarly, with DOI and the DOS included in the sample

probability = 3/10 = 0.3