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

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Intern
Joined: 08 Jan 2007
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A certain manufacturer of cake, muffin, and bread mixes has [#permalink]  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
Intern
Joined: 08 Jan 2007
Posts: 42
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thats correct, how did you get to it?
Senior Manager
Joined: 18 Feb 2007
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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
Manager
Joined: 04 Oct 2006
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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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wall street...bulls, bears, people from connecticut

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Joined: 22 Oct 2006
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A + B - Both + Neither = Total

50 + 40 - 20 + X = 100

X = 30

30/100

Manager
Joined: 12 Jun 2006
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Re: Probability [#permalink]  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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