Question

An exam is given to 100 students. The population of the class was 40 male students and 60 female students. Sixty students passed the exam. Of the students that pass the class 24 of them were men, and 36 were women. In order to get feedback on the course, a student is selected to give an interview about the exam. a. Find the probability that the student passed, given that the student is male. b. Find the probability that the student is female, given that a passing grade was received. c. Are the events the student passed the exam and the student is a man independent? d. Since more women passed the exam than men, is it more likely that a student will pass the exam if they are female?

Answer 1

This question seems very hard to me

Answer 2

Anyone can help me out!

Answer 3

ok, lets do this one problem at a time. First off, we need to understand our setting. We have one class, which is broken into two general categories: males and females. in those two categories we have passing males and failing males, and we have passing females and failing females

Answer 4

Yes that is true

Answer 5

ok, do we want these probabilities in fractions or in percents?

Answer 6

I am not sure

Answer 7

Hold on let me ask someone

Answer 8

ok, lets go with percents then. so starting with part a) we want to consider only males. We have 40 males in the class, so 40 becomes our 100% or our maximum value for the probability we are considering. of those 40 males, we know that 24 passed the exam.

Answer 9

so what percentage of our males passed the exam?

Answer 10

24%

Answer 11

ahh, now how did you get that?

Answer 12

My teacher just email me back and he said it doesn't matter if its in fractions or percents

Answer 13

Its says 24 male pass the test out of 40

Answer 14

Is that right

Answer 15

so how did you get 24%?

Answer 16

yes

Answer 17

ok, now what exactly is a percent?

Answer 18

do want me to tell you the definition

Answer 19

a percent is 1/100th of whatever our entire piece is, so if we have 100% we have the entire thing.

Answer 20

ok

Answer 21

So the main thing to notice in these types of problems is what our context is, or what our "whole piece" is for a particular problem

Answer 22

Alright

Answer 23

in part A we are told that we are only considering males, correct?

Answer 24

yes

Answer 25

so what is our entire male population? this will be our maximum value which we can then take a percent of.

Answer 26

64

Answer 27

is that right? Was I suppose to add 40+24 together

Answer 28

that's not too far off. Our population of the class is 100 people total, with 60 being female and 40 being male. of those 40 males, 24 passed the exam. So those 24 males aren't a different group, they are part of that original 40.

so if I asked you how many males failed, how would you find that out?

Answer 29

40-24 which is 16

Answer 30

is that right

Answer 31

Exactly! So of all the males, what percentage passed the exam?

Answer 32

16%

Answer 33

ok, how did you get that?

Answer 34

40-24 is how I got that

Answer 35

ok, that is how many males failed the exam. so the way to get the percentage of males that passed the exam is:

# of males that passed divided by total number of males

so: 24/40 (note: this is also the fraction form of the probability, before it is reduced)

24/40 = .6 = 60%

Answer 36

does that make any sense?

Answer 37

60% is the answer

Answer 38

Sometimes I get a little confusing with my explanations

Answer 39

ok

Answer 40

What is the answer for A just to make sure

Answer 41

The answer for A would be 60%

Answer 42

cool

Answer 43

yep! So lets try B then. We want to find the probability that a student who passed the exam was female. So what is our section of the class that we are considering?

Answer 44

60 females

Answer 45

Its says 36 pass the test

Answer 46

ok, did anyone else pass the test?

Answer 47

24 male pass the test as while

Answer 48

the wording of this one is a little vague. I think they are just trying to be confusing. Basically what it is asking is " What is the probability that a student who passed the test is female?"

does stating it that way change what you might consider our "whole piece"?

Answer 49

no

Answer 50

ok, in this case our whole piece is all the students who passed the test, we want to know, if someone passed the test, what is the likelihood that they are female? because of this we will consider all the people who passed the test and then we will break it up into males and females

Answer 51

has your teacher ever used a Venn diagram to visualize what a probability might look like?

Answer 52

yes

Answer 53

What do we do for part B

Answer 54

we will use the percent formula like this:

number of females that passed/ number of students that passed

36/60 = .6 = 60% of the students that passed were females

Answer 55

yeah I did that part already

Answer 56

ok, for part B, that is your answer

Answer 57

60% for part b

Answer 58

yep

Answer 59

ok

Answer 60

So C and D is yes or no questions

Answer 61

true. Part C just wants you to look at the definition of independent events and see if it holds in that situation

Answer 62

ok

Answer 63

and part D wants you to look at the probability that a man passed the exam and compare it to the probability that a woman passed the exam and see which is higher, if either

Answer 64

I got No for C. and Yes for D

Answer 65

is that right

Answer 66

C is correct, for D you should also have gotten no, because the probabilities are equal whether you are a man or a woman

Answer 67

that is true

Answer 68

and that should do it for that one!

Answer 69

cool

Answer 70

I have a couple more question to post than I am done

Answer 71

ok, good luck! I'll see If i find you again, I may have to go soon to do my own homework.