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Question: 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 2 of the above products?

My Answer

B1=60% B2=50% B3=35%

B1+B2+B3 = 100% B1 = 10%

Now how can I find the answer from this... I can't understand the answer they provide to this question.

Question: 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 2 of the above products?

My Answer

B1=60% B2=50% B3=35%

B1+B2+B3 = 100% B1 = 10%

Now how can I find the answer from this... I can't understand the answer they provide to this question.

Thanks in advance for the help

100 = m + c + a - (mc + ca + am) - 2 (mca) 100 = 60 + 50 + 35 - (mc + ca + am) - 2 (10) (mc + ca + am) = 145 - 100 - 20 (mc + ca + am) = 25
_________________

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Here is the theoritical equation: T = G1 + G2 + G3 - G1G2 - G2G3 - G1G3 - 2B

where: GxGy: both Gx and Gy (overlapping) B: All G1, G2, and G3 (overlapping) T: total

Derivation: Total = G1only + G2only + G3only + G1G2 + G2G3 +G3G1 + B (covering all possible groups) example: total students = only milk + only chicken + only apples + both milk and apple + both apple and chicken + both chicken and milk + all milk,chicken, and apple

G1only = G1 - G1G2 - G1G3 - B G2only = G2 - G1G2 - G2G3 - B G3only = G3 - G1G3 - G2G3 - B

plug in equations in the main equation above: Total = G1 - G1G2 - G1G3 - B + G2 - G1G2 - G2G3 - B + G3 - G1G3 - G2G3 - B + G1G2 + G2G3 + G1G3 + B Total = G1 + G2 + G3 - (G1G2 + G1G3 + G2G3) - 2B

Great explanation, THX!!!

But, If you're not so algebraic, like me =) You can also see this conceptually why this is true. Because just by looking at the derived equation, one might wonder, why? Or for me, why "-2B?" Why not just -B?

I enlightened myself by making an actual Vann diagram. With 3 post-its, I made three circles and overlapped them. Then it became so clear why the equation tells you to do -2B instead of -B or -3B

anyone like me, who just can't ACCEPT the equation as is, unless you actually SEE it, it might help.