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Foodmart customers regularly buy at least one of the

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Foodmart customers regularly buy at least one of the [#permalink] New post 29 Oct 2008, 07:59
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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 above products?


* 5%
* 10%
* 15%
* 25%
* 30%
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Re: Prop of Sets [#permalink] New post 29 Oct 2008, 08:34
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25%

I'm not entirely sure of my answer. It's my first reaction.

If we assign a number value to the shoppers, like 100 shoppers, it makes the problem a bit easier.

M = Milk (60%)
C = Chicken (50%)
A = Apples (35%)

60 people buy milk. 50 people buy Chicken, 35 people buy Apples, but we know we're counting them multiple times.

Think of them as 3 categories of groups. #1 = People that buy only 1 thing,, #2 = People that buy 2 things, and #3 = People that buy 3 things.

Assign a number of people for the group, such as 100 to make the % math easy.

Number in the group = Total number of purchases made - those that purcahsed 2 items - those that purchased all 3 items.

Number in group = 100

Total number of purchases made = 145 (60% of 100 + 50% of 100 + 35% of 100)

Those that purchased 2 items = x because this is the value we want to find

Those that purchased all 3 times = 10, but because we have 3 groups, we must make this 2 x 10 because we've counted it 3 times rather than once when adding the 60% of 100, 50% o 100, and 35% of 100. We counted it once for the milk, once for the chicken and once for the apples, when only 1 time would be correct. This is a difference of 20, so correct it by subtracting out 20.

100 = 145 - x - 20

100 = 125 - x

-25 = -x
or
x = 25
study 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 above products?


* 5%
* 10%
* 15%
* 25%
* 30%

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Re: Prop of Sets [#permalink] New post 29 Oct 2008, 08:58
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Check out this thread: 7-p508451?t=69014

There are other ways to do this problem ..... the following is a formulaic way .........

study 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 above products?


Say there are 100 customers ( we choose 100 because all the numbers given above are in percentages, picking 100 makes calculation easier)

The formula is P(A u B u C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

P(A u B u C) =100, P(A)=60, P(B)=50, P(C)=35 and P(A n B n C)=10

To determine people in exactly 2 sets(or people who buy exactly 2 items) we have to first determine P(A n B) + P(A n C) + P(B n C)

Now P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C) can be written as

P(A u B u C) = P(A) + P(B) + P(C) – { P(A n B) + P(A n C) + P(B n C)} + P(A n B n C)

we can rearrange the equation as { P(A n B) + P(A n C) + P(B n C)} = P(A) + P(B) + P(C) + P(A n B n C) - P(A u B u C)

so { P(A n B) + P(A n C) + P(B n C)} = 60 + 50 + 35 + 10 -100 = 55

We have now determined the value of { P(A n B) + P(A n C) + P(B n C)} as 55%

But this is not the number of people who are present in exactly 2 sets,

The formula for people in exactly two sets is = { P(A n B) + P(A n C) + P(B n C)} - 3P(A n B n C)
= 55-3(10) = 25%
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Re: Prop of Sets [#permalink] New post 29 Oct 2008, 09:56
Thank you - Kudos given to both.
Re: Prop of Sets   [#permalink] 29 Oct 2008, 09:56
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