Imagine Creighton has 3500 undergraduates, of which 800 belong to a fraternity o
ID: 3204533 • Letter: I
Question
Imagine Creighton has 3500 undergraduates, of which 800 belong to a fraternity or sorority ("Greeks"), and 270 are biology majors. We'll initially assume these two factors are independent.
A. What proportion of the population are Greek biology majors? (Or, to put it another way, what is the probability that an undergraduate selected at random would be a Greek biology major?)
B.What proportion are Greeks but not biology majors?
C.What proportion are neither Greek nor biology majors?
D.If we choose three students are random, what is the probability that all three will be Greeks?
E.If we choose three students are random, what is the probability that at least one will be a biology major?
F. Now we'll add chemistry majors into the mix. We'll assume there are 160 chemistry majors, and 21 of these are also majoring in biology. What is the probability that a randomly chosen undergraduate will be a chemistry or biology major (or both)?
G.An analysis of student records in indicates that Greek membership and major are not independent after all. It turns out that 87 of the 270 biology majors are Greek. Based on this data, what is the chance that a randomly chosen student will be a Greek biology major?
Explanation / Answer
A:
P(Greek) = 800 / 3500
P(Biology majors) = 270 /3500
Since these events are independent so
P(Greek and Biology major) = P(Greek)P(Biology Major) = (800/3500) * (270/3500) = 0.0176
(B)
P(Greek and not Biology Major) = P(Greek) - P(Greek and Biology major) = (800/3500) - 0.0176 = 0.2110
(C)
Out of 3500 , 3500 - (800 +270) = 2430 are neither Greek nor Biology major so
P(neither Greek nor biology) = 2430 /3500 = 0.6943
(D)
Since students are independnet from each other so the requried probability is
P(all three are Greek) = C(800,3) / C(3500,3) = 0.0119