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?
[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?
