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# Foodmart customers regularly buy at least one of the

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29 Sep 2008, 00:45
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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 above products?

What's the formula for a venn diagram of 3 circles?
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29 Sep 2008, 01:29

Have used this formula
P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)
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29 Sep 2008, 05:16
What's the formula for a venn diagram of 3 circles?

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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Last edited by amitdgr on 29 Sep 2008, 11:06, edited 1 time in total.
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29 Sep 2008, 07:32
55%

100 = 60 + 50 +35 - (any 2 things) +10

100 = 155 - any 2 things

any 2 things = 155 -100 = 55%

Am i right?

thanks
Vishal Shah
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29 Sep 2008, 07:40
amitdgr wrote:
What's the formula for a venn diagram of 3 circles?

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)
= 55-10 =45%

If formula is to deduct 3 time (A n B n C) then answer should be 25% . Isn't it?
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29 Sep 2008, 11:05
rakeshmrana wrote:
amitdgr wrote:
What's the formula for a venn diagram of 3 circles?

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)
= 55-10 =45%

If formula is to deduct 3 time (A n B n C) then answer should be 25% . Isn't it?

sorry silly mistake. Corrected in the post above.
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29 Sep 2008, 11:08
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?

What's the formula for a venn diagram of 3 circles?

100 = (60+50+35)-(x)-2(10)
x=145-120=25%
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29 Sep 2008, 18:50
x2suresh 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?

What's the formula for a venn diagram of 3 circles?

100 = (60+50+35)-(x)-2(10)
x=145-120=25%

How did you come up with the 2(10)?
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29 Sep 2008, 20:52
x2suresh 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?

What's the formula for a venn diagram of 3 circles?

100 = (60+50+35)-(x)-2(10)
x=145-120=25%

How did you come up with the 2(10)?

The formula for members in exactly 2 sets can be simplified to

P(A u B u C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) -2P(A n B n C)
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