Brittany W.

asked • 11/18/15

Probability venn diagram problem

In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained.
120 subscribe to the NYT.
151 subscribe to the WSJ.
70 subscribe to the UST.
40 subscribe to the NYT and WSJ.
30 subscribe to the WSJ and UST.
24 subscribe to the NYT and UST.
37 do not subscribe to any of these newspapers.
(a) How many of the individual investors surveyed subscribe to all three newspapers?
investors

(b) How many subscribe to only one of these newspapers?
investors

** I have set up the venn diagram, but I am totally stuck on how to find a and b! please help**

1 Expert Answer

By:

Arnold F. answered • 11/18/15

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Did your diagram look like this with all the pieces filled in with the appropriate values?
 
https://www.wyzant.com/resources/files/396074/abc_venn_diagram/download?encryptedID=VX6s8lTyNig%3D&d=v
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Brittany W.

Yes it looked like this.
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11/18/15

Arnold F.

Were you able to fill in all 8 pieces of the diagram with values?
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11/18/15

Brittany W.

I was only able to fill in what was given. How would I calculate how many people subscribe to all three?
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11/18/15

Arnold F.

If you let the "center" of the Venn diagram (I.e. ABC) equal x then you can express the other pieces in terms of x.
 
After you do that add all eight pieces together and that sum = 300. Solve the equation for x. I got x=16.
 
Try that. If you are still not sure comment back.
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11/18/15

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