Information on set theory using Venn diagram

Question

AAS PLC produces three brands of powder milk. In order to determine the marketability of this product some samples were sent out. The result of this exercise, shoes that 120 customers like brand A, 100 customers liked brand B, 110 customers like brand C, 30 customers liked brands Aand B, 25 customers like brand B and C, 20

customers liked brands A and C and the same

number of those who customers that liked all the three brands also dislike all the brands . In a

sample of 275 customers how many of them

 like

1. Brands,A,B and C?

2. Brands A or B but not C?

3. Brands B and C but not A?

4. One brand only?

Answer 1

Given: AAS PLC produces three brands A, Bandc thmath of powder milk.

A = liked customer 120, \(\therefore \) A = 120

B = liked customer 100, \(\therefore \) B = 100

C = liked custimer 110, \(\therefore \) C = 110

And,

A and B = liked customers 30, \(\therefore \) A + B = 30

B and C = liked customers 25, \(\therefore \) B + C = 25

A and C = liked customers 20, \(\therefore \) A + C = 20

A + B + C = liked customers 20, \(\therefore \) A + B + C = 20

A + B + C = disliked customers 20,  \(\therefore \) A + B + C (dislike) = 20

To find: In a sample of 275 customers, How many of them liked.

Solution: Showing by venn diagram,

\(\therefore \) A = 30 + 20 + 20 + 50 = 120

\(\therefore \) B = 30 + 25 + 20 + 25 = 100

\(\therefore \) C =  20 + 20 + 25 + 45 = 110

1. 20 customers like

2. 30 customers like

3. 25 customers like

4. 120 customers like

Comments

NishkarshGupta, hello

Unfortunately, your Venn diagram only represents (50+30+20+20+25+25+45+20) 235 customers when the problem says that there was a sample of 275 customers.  In a Venn diagram, all of the sample size must be represented.

I looked at this problem and it is not possible to do given the constraints the way that they are worded.

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If you have an explanation please provide ......

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Nishkarnshgupta, hello
According to the Venn diagram you drew:
50 customers like just brand A,
25 customers like just brand B,
45 customers like just brand C,
30 customers like both brand A and brand B,
25 customers like both brand B and brand C,
20 customers like both brand A and brand C,
20 customers like brand A, brand B, and brand C, and
20 customers do not like any of the brands

Your diagram only represents 235 customers!?
But.....the population sample was 275 customers.