redbeanaddict wrote:

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

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7-p508451?t=69014redbeanaddict 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?

Is the answer 45% ?

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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