Question

Among a group of people, 40% liked red, 30% liked blue and 30% liked green. 7% liked both red and green, 5% liked both red and blue, 10% liked both green and blue. If 86% of them liked at least one color, what percentage of people liked all three

Answer 1

Answer:

8%   ( but Question data is not correct)

Step-by-step explanation:

Red = 40 %

Green = 30%

Blue = 30%

RED∩BLUE = 5 %

RED∩GREEN = 7%

BLUE∩GREEN = 10%

people liked all three at least one color

= RED + BLUE + GREEN - RED∩BLUE - RED∩GREEN - BLUE∩GREEN + RED∩BLUE∩GREEN

=>  86 = 40 + 30 + 30 - 5 - 7 - 10 + RED∩BLUE∩GREEN

=> 86 = 78 + RED∩BLUE∩GREEN

=> RED∩BLUE∩GREEN = 8

percentage of people liked all three = 8 %

But % of People liking all three games can not be more than % Of people liking two games  ( 5 %  &  7 % )

as R∩B∩G  would be subset of R∩B  & R∩G

so data provided is Wrong

Max people who liked atleast one color can be 83 % then people liked all three = 5 %

Min people who liked atleast one color can be 78% then people liked all three = 0 %