CFA Practice Question

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CFA Practice Question

A dormitory on campus houses 200 students. 120 are male, 50 are upper-division students, and 40 are upper-division male students. A student is selected at random. The probability of selecting a lower-division student, given the student is female, is ______.
A. 7/8
B. 7/20
C. 2/5

User Contributed Comments 24

User Comment
mtcfa PLease help; very confused on this one.
n9845705 If the probability of selecting even just 1 female student was 7/8, then there would have to be 175 women out of 200 total people. Since there is 120 males this cannot be the answer. Someone help!
tenny45 I think this is how it works:
We know that there are 80 female total.
We know that there are 10 upper division female (50-40 = 10)
Therefore: 1-(10/80) = 7/8

Let me know if you find any other ways to do it.
yly13 we got 80 females, 10 upper female students, so 70 female lowers. Thus as long as you are selecting from 80 females, ratio would be 70/80
volkovv yly13 is precisely correct:

since you have 80 females, and you know that 10 of them are upper (50-40) that leaves you with 70 lower, so chances that a student will be lower given that she is female is 7/8
chuong P of select Femalesis given = 1. and P of upper femail = 10/80 -> P of lower females = 1-10/80 => 7/8
gene80 think one quick way of doing this is first to note that a majority of females are in Lower Division. Hence given that a female was chosen, we can logically guess that the chances of her from a Lower Division is very high!
sevaa1 This is how I approached this question: We know there are 200 students in the class, 120 of the are male. Thus, there are 80 female students in the class. There is only one answer that has 8 in the denominator: a). Sometimes it's jumping to conclusions, sometimes it can save time...
labsbamb good on this one
willdo1241 Greatly appreciate all the comments posted!! They all very helpful!!
FCFA This is why I love analyst notes, only peers can explain well, thanks all.
BullsEye got tricked. Key is "given student is female".
kamil77 Bayes theorem: P(A/B) = P(A)x P(B/A)/P(B)
A - probability that a student is lower division one
B - probability that a student is female
P(A) = 150/200 = 3/4
P(B) = 80/200 = 2/5
P(B/A) = 70/150 = 7/15
P(A/B) = (3/4)x(7/15)/(2/5) = 7/8
capitalpirate use a 2x2 grid: column1: male, c2:female
row1: upper, r2: lower... fill it in with info!
Yurik74 that's good one
migena thanks for all the comments posted!
podobed the main thing to worry about - to read question very carafully
Shammel Like BullsEye said the key is "given the student is a female."
jmumm What I find difficult when taking these online exams is that I can't circle key words/phrases like "given the student is a female." I forget these details as I'm punching out calculations.
bantoo don't complicate using Bay's theorem
Shaan23 Stats guy again. You have to use bayes to make it easy on yourself.

We want P(Lower) = P(lower/Male)*P(Male) + P(Lower/Female)*P(Female)

We want to solve the P(lower/female) for this question. Everything else is easy to plug in with the exception of P(lower/Male) which requires a little bit of thought.

P(lower/male) = P(Male and Lower) / P(male)

If for a stats guy this takes a bit of time but if you actually do everything I just it on paper with numbers you'll have Bayes theorem down. It doesnt get more complicated then this. Its just annoying.
farhan92 i used a tree diagram for this one but read the queston wrong (basically answered the question i wanted to answer!)
sparis02 A simple way of looking at it..

F= Female L= Lower
M= Male U= Upper

M=120 so.. F=80
U=50 so... L=150
UM= 40
F = FU + FL
80= FU + FL

M= MU + ML
120 = 40 + ML

STEP (1) Solve for ML: M - MU = ML therefore 120-40= 80 so ML=80

U= FU + MU
50 = FU + 40

L = FL + ML
150= FL + ML

STEP (2) Solve for FL: where ML was solved in STEP (1) and equals 80... so... FL=L-ML 150-40=70

there are 70 Female students in the Lower Division

adding probabilities...
P(L|F) = P(FL)/P(F)
P(F)= F/200 = 80/200 = .4 ( we know the answer cannot be C)

P(FL) = FL/200 = 70/200 = .35 (we know the answer cannot be B)

therefore the answer is A.. lets solve to make sure

P(L|F) = P(FL)/P(F) = .35/.4 = .857
mlaique P(LD given F) = P(LD & F) / P (F)
P(LD given F) = (70/200) / 80/200) = 7/8
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