Among a group of people, 40% like 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
Answers
Answer:
The correct answer is 8℅.
Step-by-step explanation:
This can be solved using a Venn diagram( attached below).
Percentage liking at least one colour is 86℅ so the rest 14℅ did not like any colour and hence lies in the outer space.
On adding the three percentages of red, blue and green we get= 100℅ but this should be 86℅.
The extra 14℅ is due to the common parts(which got counted twice)- Red+Blue, Blue+Green and Red+Green and all three( considered as X here)
So, the ones who liked at least one colour = 100℅ - 7℅+5℅+10℅ + X℅ = 100℅- 22℅ +X = 86℅
So, X℅ = 8.
Answer:
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 %