A campus program evenly enrols 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)0.0256
B)1.00
C)0.0625
D)0.16

Question

Quizplus · Accepted Answer

We can solve this problem by using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
n = 4 (sample size)
k = 4 (number of successes)
p = 0.5 (probability of success, i.e. being an undergraduate student)

Substituting the values:
P(X=4) = (4 choose 4) * 0.5^4 * (1-0.5)^(4-4)
= 0.0625

Therefore, the probability that all 4 selected students are undergraduate students is 0.0625 or 6.25%. The best choice is C.

A Campus Program Evenly Enrols Undergraduate and Graduate Students