SOLUTION: I am having problems with doing Venn Diagrams, I really need your help with this??? Please? Okay, here's the question:
A drug company is considering manufacturing a new product
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Question 184317This question is from textbook A Survey of Mathematics with Application
: I am having problems with doing Venn Diagrams, I really need your help with this??? Please? Okay, here's the question:
A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 120 people. The results are as follows:
62 liked cherry flavor
74 liked orange flavor
35 liked both flavors
We're asked to construct a Venn Diagram and answer the following:
a.) How many liked only orange flavor
b.) How many liked only cherry flavor
c.) How many like either one or the other or both
This is pretty confusing to me, i'm now sure if i'm making too much out of this or what i'm doing, but I definitely need some help
This question is from textbook A Survey of Mathematics with Application
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 120 people. The results are as follows:
62 liked cherry flavor
74 liked orange flavor
35 liked both flavors
------------
Procedure:
Draw two circles that overlap.
Label one of them orange; Label the other cherry.
Total on cherry is 62 ; Total on orange is 74
Put a 35 in the overlap section.
Then the rest of the orange circle has 74 - 35 = 39 orange in it.
Also the rest of the cherry circle has 62 - 35 = 27 cherry in it.
-------------
All of that is the Venn Diagram you need.
--------------
We're asked to construct a Venn Diagram and answer the following:
a.) How many liked only orange flavor
Ans: 39
--------
b.) How many liked only cherry flavor
Ans: 27
--------
c.) How many like either one or the other or both
Ans: Add 27 + 39 + 35 = 101
=============================================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Draw a big rectangle. That represents everybody that was surveyed; according to your givens, 120 people.
Draw two circles inside of the rectangle and make sure they overlap some. That divides the area inside of your rectangle into four regions: An area outside of both circles, an area that is ONLY in the first circle, an area that is ONLY in the second circle, and a little lozenge shaped area that is inside of BOTH circles.
The lozenge-shaped area represents the 35 people who liked both cherry and orange, so write the number 35 in that area.
Next pick one of the circles to represent cherry and the other will then represent orange. You know that 62 people liked cherry, but 35 of those people also liked orange, so subtract 35 from 62 = 27 to get the number of people who ONLY liked cherry. Write that number inside the 'cherry' circle but outside of the lozenge-shaped area. Similarly, 74 - 35 = 39 people ONLY liked orange. Write that number in the 'orange' circle but outside of the lozenge shaped area.
Now you can answer your questions directly:
Only liked Cherry: 27
Only liked Orange: 39
Liked one OR the other OR both: 27 + 39 + 35:
Answers to questions not asked here but that might come up if you discuss this one in class:
Liked one or the other but NOT both: 27 + 39.
Didn't like either: 120 - (27 + 39 + 35)
Didn't like orange: 120 - 39
Didn't like both: 120 - 35
Very handy things are Venn diagrams.
Super-Double-Plus Extra Credit What would the diagram look like (without the numbers) if your survey included 3 flavors?
John
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