Question 197947: I am really confused about this, please help me so that I can understand. Thank you
In a survey of 100 consumers, 33 indicated that they were going to buy a new car, 18 said they were going to buy a new refrigerator, and 34 said they were going to buy a new washer. Of these, 7 were going to buy both a car and a refrigerator, 15 were going to buy a car and a washer, and 9 were going to buy a washer and a refrigerator. Three consumers indicated that they were 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?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw three circles that overlap such that there is an area in the center that is part of all three circles. Label the circles C, R, and W.
There are 3 people who will purchase all three items, so put a 3 in the center area that is part of all three circles.
There are 7 people who are going to buy both a car and a refrigerator, but that includes the 3 people who are buying all three, so that leaves 4 that are ONLY buying a car and a refrigerator. Put a 4 in the area where just the C circle and the R circle overlap.
Using the same sort of logic, the area of overlap between the W and R circles gets a 6, and the overlap between the C and W circles gets a 12.
Now, 12 plus 3 plus 4 = 19 is the number of people who are going to buy a car and something else, so 33 minus 19 = 14 is the number that is only going to buy a car. So 14 goes in the part of the C circle that has no overlap.
Likewise, you get a 5 in the no-overlap part of the R circle, and a 13 in the no-overlap part of the W circle.
Now, using your diagram, you can start to answer the questions.
Only a car: the number in the non-overlap part of the C circle
Only a washer and only a refrigerator -- you should be able to do these yourself.
A car and a washer but not a refrigerator. The part of the diagram where circles C and W overlap but not including the center part that is also included in circle R.
None of these items. Add up all the numbers in your diagram, you should get 57. But the survey was taken from 100 people, so 100 - 57 = ?
Here's a picture of the diagram before you start filling in the information.
John
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