SOLUTION: Please help me with the following questions.I dont understand what Im doing. In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were g

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Question 184848: Please help me with the following questions.I dont understand what Im doing.
In a survey of 75 consumers, 12 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 24 said they were going to buy a new washer. Of these, 6 were going to buy both a car and a refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy a washer and a refrigerator. One person indicated that she was going to buy all three items.
Construct a Venn diagram, label your diagram clearly. Use your diagram to answer the following questions:
(a) How many were going to buy only a car?
(b) How many were going to buy only a washer?
(c) How many were going to buy only a refrigerator
(d) How many were going to buy a car and a washer but not a refrigerator?
(e) How many were going to buy none of these items?
Please help me
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What you have to draw is 3 interlocking circles with
an area in the middle which is common to all 3.
Kind of like the olympic rings.
1 ring will be consumers who bought refrigerators
1 ring will be consumers who bought cars
1 ring will be consumers who bought washers
All the small and big areas making up the rings adds up to
the total number of people buying items
Right away I'm told that the car ring contains 12 people,
the fridge ring contains 18 people, and the washer ring
contains 24 people
What I do is label each ring just outside of it like this:
c=12
f=18
w=24
Of these, 6 were going to buy both a car and a refrigerator
Locate the small area where c and f overlap, and put a 6
inside it.
4 were going to buy a car and a washer.
This is the area common to c and w. Put a 4 inside it
10 were going to buy a washer and a refrigerator
Label the intersection of w and f with a 10
One person indicated that she was going to buy all three items.
This last fact gives you all the answers. It's the key.
The intersection of c and f = 6, but 1 of those is the last
person, so 6 - 1 = 5 persons will buy ONLY both f and c.
10 - 1 = 9 persons will buy ONLY both w and f.
4 - 1 = 3 persons will buy ONLY both w and c.
Now you should be able to label every area on the diagram
(a) How many were going to buy only a car? 3
(b) How many were going to buy only a washer? 11
(c) How many were going to buy only a refrigerator 3
(d) How many were going to buy a car and a washer but not a refrigerator? 3
(e) How many were going to buy none of these items? 40
I come up with a total of 35 persons buying items
c = 3
w = 11
f = 3
w+c DISABLED_event_only= 3
f+c DISABLED_event_only= 5
w+f DISABLED_event_only= 9
All 3 = 1
------------
35 total
The trick is not to count the sme area twice.
Hope I got the right answers and my method helps you

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution with Venn Diagram:

In a survey of 75 consumers, 12 indicated that they were going to buy a new
car, 18 said they were going to buy a new refrigerator, and 24 said they were
going to buy a new washer. Of these, 6 were going to buy both a car and a
refrigerator, 4 were going to buy a car and a washer, and 10 were going to buy
a washer and a refrigerator. One person indicated that she was going to buy all
three items. 

First draw a big square or rectangle to hold all 75 consumers:
 
drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4) )
 
Next draw a circle to hold all 12 consumers who said they
were going to buy a new car and label it C (for "car"):
 

 
Next draw a circle overlapping the first to hold all 
18 consumers who said they were going to buy a refrigerator and label
it R. (The overlapping part will contain the consumers who said
they were going to buy a new car and a refrigerator).
 

 
Next draw a circle overlapping the first two circles
to hold all the consumers who said they were going to
buy a new washer and label it W: 
 

 
This gives us 8 regions to classify cnsumers with
according to what they said they were going to buy:
 
There is only one statements which immediately give 
us complete information about any of the 8 regions are these:
 
This one:

>>...One person indicated that she was going to buy all
three items...<<

So we will fill 1 in the middle region which is the
only region common to all three circles:


Next we look at this statement
 
>>...6 were going to buy both a car and a refrigerator...<<
 
These 6 are in the region where circles C and R overlap.
There is already 1 accounted for in there, so we write
the other 5 of the 6 in the other part of the overlapping 
part of C and R:


 
-----

Next we look at this statement
 
>>...4 were going to buy a car and a washer...<<
 
These 4 are in the region where circles C and W overlap.
There is already 1 accounted for in there, so we put
the other 3 of the 4 in the other part of the 
overlapping part of C and W:



-----

Next we look at this statement

>>...10 were going to buy a washer and a refrigerator...<<
 
These 10 are in the region where circles W and R overlap.
There is already 1 accounted for in there, so we put
the other 9 of the 10 in the other part of the overlapping 
part of W and R:



-----
Next we look at this statement

>>...12 indicated that they were going to buy a new car...<<
 
These 12 make up the total in the entire circle C
There are already 5+1+3 or 9 of these 12 accounted for 
in circle C, so we put the other 3 of the 12 in the 
upper left part of circle C:



-----

Next we look at this statement

>>...18 said they were going to buy a new refrigerator...<<
 
These 18 make up the total in the entire circle R.
There are already 5+1+9 or 15 of these 18 accounted for 
in circle R, so we put the other 3 of the 18 in the 
upper right part of circle R:



-----

Next we look at this statement

>>...24 said they were going to buy a new washer...<<
 
These 24 make up the total in the entire circle W.
There are already 3+1+9 or 13 of these 24 accounted for 
in circle W, so we put the other 11 of the 24 in the 
lower part of circle W:



-----

Next we look at these words:

>>...In a survey of 75 consumers...<<
 
Now we see how many of the 75 consumers we
have accounted for.  They are

3+5+3+3+1+9+11 or 35, so there are 75-35 or
40 more of the 75 left to account for.  These
40 are outside all the circles.  So let's
write 40 in the region outside all the
three circles, but inside the rectangle.  I'll
put it in the bottom left, although it could go
anywhere in that outer region.



Now we can answer the questions:

(a)	How many were going to buy only a car? 

These are the 3 in the upper left region of circle C.

(b)	How many were going to buy only a washer? 

These are the 11 in the lower region of circle W.

(c)	How many were going to buy only a refrigerator

These are the 3 in the upper rightt region of circle R.

(d)	How many were going to buy a car and a washer but not a refrigerator? 

These are the 5 in the region in the middle above which
is part of bot circles C and R but not part of W.

(e)	How many were going to buy none of these items?

These are the 40 which are outside all the circles.

Edwin