A certain manufacturer of cake, muffin, and bread mixes has 100 buyers

Question

A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?

A. 1/10
B. 3/10
C. 1/2
D. 7/10
E. 9/10

Show Answer

Official Answer

B

A. 1/10 
B. 3/10 
C. 1/2 
D. 7/10 
E. 9/10

Bunuel · Accepted Answer

A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix? 
A. 1/10 
B. 3/10 
C. 1/2 
D. 7/10 
E. 9/10

Total = {cake} + {muffin} - {both} + {neither}

100 = 50 + 40 - 20 + {neither}  -->  {neither} = 30  -->  \frac{neither}{total}=\frac{30}{100}=\frac{3}{10} .

Answer: B.

Hope it helps.

petrifiedbutstanding · Answer

Bunuel,

I have a question. I got this right, but I still think I'm missing something. If you considered this in a Venn-diagram format, it would be clear that there can be buyer who purchase cake mix and bread mix or muffin mix and bread mix. This would alter the equation somewhat. And I noticed that you didn't consider this. Can you please explain why?

Bunuel · Answer

I'm not sure that I understand what you mean.

We are told that "A certain manufacturer has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix."

So,  Total = {cake} + {muffin} - {both} + {neither}  -->  100 = 50 + 40 - 20 + {neither}  -->  {neither} = 30 .

What should be altered above and why?

narangvaibhav · Answer

Do we need to consider "neither" case in all such set theoory questions?

petrifiedbutstanding · Answer

You're right actually. I considered buyers of the bread mix as well, which is clearly not necessary in the problem.

cyberjadugar · Answer

Hi,

Referring to the following venn diagram, the area marked in grey represents the buyers who purchases neither cake mix nor muffin mix.
=100-70
=30

Attachment:

venn3.jpg [ 10 KiB | Viewed 25016 times ]

Thus, probability = 30/100 = 3/10

Answer (B)

Regards,

fozzzy · Answer

Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?

Bunuel · Answer

In order {neither} to make sense. We are told there are 100  buyers . Neither cake mix nor muffin mix byers must be  buyers  of something else.

Hope it's clear.

Skag55 · Answer

I got confused too, the "bread mix" is not necessary to be mentioned (could be cookies, or pasty, you name it), it's just confuses.
What it really is, is a 2x2 matrix as shown in the picture.

keats · Answer

Yes, this makes sense. I was looking for an answer to the same question. Your point helps here,  Bunuel

esonrev · Answer

This is a bit confusing in that it never mentions the 50 buyers of cake (or 40 of muffin) are included in the 20 that purchase both

jabhatta2 · Answer

Hi  Bunuel  -- If 20 buyers buy cake and muffin mix -- in my three way venn diagram -- is 20 equal to area 1 + area 4 or is 20 equal to area 1 only ?

I tried solving this on a three way overlapping set and was not sure, where the "20" would go

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A certain manufacturer of cake, muffin, and bread mixes has 100 buyers

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A certain manufacturer of cake, muffin, and bread mixes has 100 buyers

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