Question 598171: A small university surveyed 77 of its freshmen business students. the students were asked whether they read Business Week (BW), The Wall Street Journal (WSJ), or Fortune. The results of the survey are below:
25 of the students read BW
27 do not read Fortune
19 read The WSJ
9 read all three
13 read BW and Fortune
11 read BW, but not The WSJ
11 read The WSJ and Fortune.
a. Create the Venn Diagram associated with this problem.
b. How many students read Fortune only?
c. How many students read either Business Week or Fortune?
Please and Thank you. :)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw a large rectangle. Inside of the rectangle draw 3 overlapping circles so that you create 8 regions inside of the rectangle. Lable the three circles as BW, WSJ, and F.
In the region at the center common to all three circles put a 9 representing the 9 students that read all three publications.
Since the 13 that read BW and F includes the 9 that read all three, put a 4 in the region where the BW circle only overlaps the F circle. Likewise the WSJ and F overlap gets a 2.
Since 11 read BW but not WSJ, the "by itself" part of the BW circle plus the overlap with the F circle must add up to 11. Therefore put a 7 in the "by itself" part of the BW circle.
Since there were 77 students surveyed and 27 do NOT read F, the 4 regions of the F circle must add up to 77 minus 27 equals 50. You already have 4 plus 9 plus 2 = 15, so 35 goes in the "by itself" part of the F circle.
Since 25 read BW, the four parts of the BW circle must add up to 25. You already have 7 plus 4 plus 9 = 20, so put 5 in the BW/WSJ overlap.
If you add all of the numbers that you have entered so far, you get 65. That means that 77 minus 56 = 12 students do NOT read ANY of the three publications. Write a 12 in the rectangle outside of all of the circles.
From the information you have entered in the Venn diagram we just developed, you should be able to answer the other two questions pretty directly.
John
My calculator said it, I believe it, that settles it
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