Which Overlapping Set Formula to Apply?

[bryan22583]

Q: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

[spoiler]A: 10% [/spoiler]

I believe that answer is derived by applying (A+B+C) - (AB + AC +BC) - 2(ABC) + Neither. However, since we don't know the amount who liked exactly 2 products, it appears to me that the applicable formula should be: (A+B+C) - (AB +AC+BC) + (ABC) + (Neither), which would yield an answer of [spoiler]25%.[/spoiler]

Am I missing something? How can I deduce which formula to apply to questions like these?

[snigdha1605]

There are two formulas for Overlapping Sets -

Formula 1 -

Total = A + B + C - (Sum of 2-group overlaps) + (All three overlap) + Neither

Formula 2 -

Total = A + B + C - (Sum of Exactly 2-group overlaps) - 2* (All three overlap) + Neither


In the above question, the Second formula is to be used where you can calculate the % of people who like exactly 2 groups. (Let this be x)

From this ,

The percentage of the survey participants liked more than one of the three products =
%who like exactly 2 product + % who liked 3 products
= 5+ 5
= 10 %

Hope this helps!

Regards,
Snigdha

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