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

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A certain manufacturer of cake, muffin, and bread mixes has [#permalink] New post 27 Feb 2007, 17:00
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 muffine mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the selected will be one who purchases neither cake mix nor muffine mix?

1/3
3/10
1/2
7/10
9/10
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 [#permalink] New post 27 Feb 2007, 17:07
thats correct, how did you get to it?
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 [#permalink] New post 27 Feb 2007, 17:12
just C = 50-20 = 30
just M = 40-20 = 20
Both = 20

Total - (C+M+Both) = Neither
100-(30+20+20) = 70

Neither/Total = 30/100 = 3/10
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 [#permalink] New post 27 Feb 2007, 21:22
Yeah the short way is when you recognize problems like this you can just do (individual + individual - combined)

so 50+40-20 = 70

100-70 = 30

30/100 = 3/10
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 [#permalink] New post 27 Feb 2007, 21:34
A + B - Both + Neither = Total

50 + 40 - 20 + X = 100

X = 30

30/100

3/10 Answer
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Re: Probability [#permalink] New post 01 Mar 2007, 19:17
cucrose wrote:
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 muffine mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the selected will be one who purchases neither cake mix nor muffine mix?

1/3
3/10
1/2
7/10
9/10
For these kind of problems, I would rather make a Venn diagram and solve for the unknown quantity. This is a great question in which both concepts are tested i.e. usage of Venn diagrams and probability.
Re: Probability   [#permalink] 01 Mar 2007, 19:17
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