Question

A local university wanted to understand what students prefer to eat during finals. They asked 1000 students, "Do you prefer chicken, burgers, or pizza?" The results of the survey are shown in the two-way table below:


Chicken Burgers Pizza
Male 127 218 125
Female 219 192 119


What is the probability that a person chosen at random from this survey prefers pizza given that they are female? Round your answer to the nearest tenth.
@mathmale

Answer 1

this is another problem in conditional probability, even though it looks a lot different from the one we did just before.

Answer 2

The table is a little hard to read because the numbers are not lined up in neat columns, but see whether we can work on it anyway. We could always re-type the table if need be.

Answer 3

Please add together the 3 numbes in the 1st row of numbers: Add up 127,218 and 125. Write the sum to the right of that 125.

Answer 4

I'd be glad to continue helping you with this if you have the interest. But I'd need to hear back from you first.

Answer 5

the sum is 470.. Im very sorry once again.. @mathmale

Answer 6

I did lots of other things myself, mainly helping other on OpenStudy.
Just a sec...I'll be right with you.

Answer 7

Right: that sum is 470.
Now do the same thing with the second row. Add up those 3 numbers and write your result (the sum) to the right of the 119 in the second row.

Answer 8

530 and 470

Answer 9

Yes. the sum of the 1st row is 470 and the sum of the 2nd row is 530. Agreed.
Now, if you'll please add 530 and 470 together, you'll get what? Think carefully; look at the problem what would that sum represent?

Answer 10

1000

Answer 11

but I don't know what it represents

Answer 12

Yes, it's 1000, but that represents the total number of students.
I know this is boring, but please now add up all 3 columns and write the respective sums at the bottom of each column.

Answer 13

woohoo: there are 470 male students and 530 female students, so the sum (the number of students) is 1000.

Answer 14

chickens burgers pizza
346 410 244

Answer 15

@mathmale

Answer 16

You there @mathmale

Answer 17

I'm sorry, I did type something to you, but evidently it did not go thru to you.
I've asked you to add up those last 3 numbers, and to tell me what the sum represents.

Answer 18

1000 and i dont know what it represents. @mathmale

Answer 19

woohoo, I will not abandon you. I'm sorry I'm sometimes slow in responding, but rest assured I will help you to finish solving this problem.

Answer 20

lol ok. but pls

Answer 21

On the extreme right you have the total numbers of male and female students, right?

Answer 22

In the bottom margin you have the numbers of students who prefer chicken, pizza and whatever else, right?
So in every case those numbers represent numbers of students.

Answer 23

the gender and this the catergories

Answer 24

I have no idea what 's happening here:

I typed a whole table on your behalf and that entry has not posted here.

Answer 25

I don't see the chart you made

Answer 26

C B P Totals
M 127 218 125
F 219 192 119
----------------------------------------------

Answer 27

copy that and then finish the table. You've already done all of the calculations.
copy my diagram, paste it in your response window and finish it, please.

Answer 28

C B P Totals
M 127 218 125 470
F 219 192 119 530
whats exactly the point for this chart? @mathmale

Answer 29

I warned you that it's boring work, but it's essential work.

You haven't finished the last row, which is made up of four totals.
but to answer this particular question, you don't need that very last row that you haven't typed in yet. Pls go back and re-read the original question then we will return to this chart and answer that question.

Answer 30

Here's the question:

What is the probability that a person chosen at random from this survey prefers pizza given that they are female?

Look in the FEMALE

Answer 31

look in the female row, the 2nd row of numbers. How many females are there, total?

Answer 32

Now how many of those females prefer pizza?

Evaluate that number divided by the total number of females; ignore ALL of the other data.

Answer 33

the good news is that if y ou complete this correctly, you've solved the entire problem. Done! Done!

Answer 34

Here is the chart I made earlier:

C B P Totals
M 127 218 125
F 219 192 119 530
----------------------------------------------

Answer 35

C B P Totals
M 127 218 125 470
F 219 192 119 530
1000

Answer 36

the number of females who prefer pizza is ....

the total number of females is ....

The ratio of (number of f who prefer pizza) TO (TOTAL NUMB ER OF F) IS WHAT?

Answer 37

lOOK AT THE 2ND row of your chart, above.
Ignore all the other info.

Answer 38

the number of females who prefer pizza is .... ?

Answer 39

192;530

Answer 40

Wasn't it 119 f who prefer pizza? 192 is the number of f who prefer b, what ever that is.

Answer 41

the number of females who prefer pizza is .... ?

Answer 42

119:530

Answer 43

the total number of f is 530 (you're correct)

the ratio 119/530 is the answer you want: it's the probability that the student will prefer pizza, GIVEN THAT THE STUDENT HAPPENS TO BE FEMALE.
YES, EXACTLY.

now use your calculator to divide 119/530.

Answer 44

0.22452

Answer 45

the result, 0.2245, or 0.225, is that probability. if you grab one student from those 1000, sight unseen (at random), and then discover that the student is female :) then the probab. that that student wants pizza is 0.2245, or 0.225.

that is it. all done.

Can y ou answer your own question, "What's the point of adding up all those numbers?"

Answer 46

times that by 100 and you get 22.5%

Answer 47

yes.

Answer 48

thank you!

Answer 49

Wonderful. There's a lot more to contingency tables such as the one we created.

Answer 50

If you have time later on, pick another problem that comes with a table like that and we will explore other possibilities.

All the best to you; see you again soon!! MM