SOLUTION: please please help thank you so much 1.A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 150 people.

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Question 198368: please please help
thank you so much
1.A drug company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 150 people. The results are as follows:
75 liked cherry flavor
94 liked orange flavor
22 liked both flavors.
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 liked either one or the other or both?
d)How many liked neither?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's draw a venn diagram and fill in the proper values (see below).



Since 22 liked both, this means that the number 22 goes in the center. Since 94 liked orange and 22 liked both, this tells us that 94-22=72 liked orange only. So place this in the right circle. Likewise, because 75 people liked cherry and 22 liked both, this means that 75-22=53 people only liked cherry. So the number 53 goes in the left circle.

So how many people have we counted so far? Let's find out: simply add up the values to get: 22+53+72=147


So 147 people either liked one flavor or the other (or both)


Now we're given that 150 people participated. So this means that 150-147=3 people did not like either flavor.


So the value 3 goes outside both circles into the rectangle. So when everything is said and done, you should have something similar to this




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Now let's use the venn diagram to answer the questions:

a) How many liked only orange flavor? 72 people

b) How many liked only cherry flavor? 53 people

c) How many liked either one or the other or both? Just add up all of the values that lie in either circle to get: 72+22+53=147. So 147 people like either flavor or both flavors. An alternative is to subtract the number of people who did not like any flavor from the total (to get the same answer).

d) How many liked neither? From the venn diagram, we see that 3 people did not like either flavor.