- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 2. Unconditional, Conditional, and Joint Probabilities

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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

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**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 Hence, 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 Given: 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 |