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Foodmart customers regularly buy at least one of the following product [#permalink]

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02 Mar 2010, 19:45

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Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either -

Even though this is not a typical 2-group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N - B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N - B - T*(3-1) , where T is members of three groups and B is members of only two groups.

There is no neither group because all customers purchase at least one product. The correct answer is D.

I suspect the formula for three overlapping sets used in the question. Can someone confirm it.

Re: Foodmart customers regularly buy at least one of the following product [#permalink]

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02 Mar 2010, 21:36

BarneyStinson wrote:

Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

A) 5% B) 10% C) 15% D) 25% E) 30%

I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either -

Even though this is not a typical 2-group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N - B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N - B - T*(3-1) , where T is members of three groups and B is members of only two groups.

There is no neither group because all customers purchase at least one product. The correct answer is D.

I suspect the formula for three overlapping sets used in the question. Can someone confirm it.

The formula is n(AUBUC) = n(A)+n(B)+n(C)-B+A-N where B is both (it will sum of (A&B), (B&C), (C&A)). and A is All and N is neither so plugging in we get 100 = 60+50+35+10-B-0 B = 55. exactly two = 55 - 3(10) = 25 subtracting 10% three times as this value is including in all the (A&B), (B&C), (C&A).

Re: Foodmart customers regularly buy at least one of the following product [#permalink]

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04 Mar 2010, 22:01

bangalorian2000 wrote:

The formula is n(AUBUC) = n(A)+n(B)+n(C)-B+A-N where B is both (it will sum of (A&B), (B&C), (C&A)). and A is All and N is neither so plugging in we get 100 = 60+50+35+10-B-0 B = 55. exactly two = 55 - 3(10) = 25 subtracting 10% three times as this value is including in all the (A&B), (B&C), (C&A).

Gotcha bro!!! You are indeed smart!!! _________________

Re: Foodmart customers regularly buy at least one of the following product [#permalink]

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15 Nov 2014, 00:40

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Re: Foodmart customers regularly buy at least one of the following product [#permalink]

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15 Nov 2014, 04:58

Expert's post

BarneyStinson wrote:

Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either -

Even though this is not a typical 2-group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N - B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N - B - T*(3-1) , where T is members of three groups and B is members of only two groups.

There is no neither group because all customers purchase at least one product. The correct answer is D.

I suspect the formula for three overlapping sets used in the question. Can someone confirm it.

100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

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