- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 2. Unconditional, Conditional, and Joint Probabilities
CFA Practice Question
There are 985 practice questions for this topic.
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 ______.
User Contributed Comments 24
|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 wrote...do 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
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
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