A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
A) 1.00
B) 0.16
C) 0.0625
D) 0.0256

Question

Quizplus · Accepted Answer

There are only 2 types of students: undergraduate and graduate, each with 50% probability of being selected. Since the selection is without replacement, the probability of selecting an undergraduate student decreases with each selection. The probability that the first student selected is an undergraduate is 0.5. The probability that the second student selected is an undergraduate given that the first was an undergraduate is 0.4 (since there are now more graduate students left in the program). Similarly, the probability that the third student selected is an undergraduate given that the first 2 were undergraduate is 0.33 and the probability that the fourth student selected is an undergraduate given that the first 3 were undergraduate is 0.25. Therefore, the probability that all 4 randomly selected students are undergraduate is: 
0.5 x 0.4 x 0.33 x 0.25 = 0.0625 (or 6.25%)

A Campus Program Evenly Enrolls Undergraduate and Graduate Students