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Bunuel
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.

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?

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

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?

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?

You're right actually. I considered buyers of the bread mix as well, which is clearly not necessary in the problem.
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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
venn3.jpg [ 10 KiB | Viewed 26054 times ]

Thus, probability = 30/100 = 3/10

Answer (B)

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

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.
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fozzzy
Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?
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.
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gmat.png
gmat.png [ 6.56 KiB | Viewed 24604 times ]

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

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.

Yes, this makes sense. I was looking for an answer to the same question. Your point helps here, Bunuel
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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
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Bunuel
fozzzy
Why does the question mention bread mixes? What's the purpose of that if it isn't used to solve the problem?

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.

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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Three way overlapping set.JPG [ 32.16 KiB | Viewed 16504 times ]

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