Question

Q. In a sample survey it is found that 53%
of the respondents prefer brand A of tea,
61% brand B, 60% brand C, 24% prefer A
and B, 35% B and C, 27% A and C, 5% liked
none of these brands. How many prefer all
the three brands?

Answer 1

Given info : In a sample survey it is found that 53% of the respondents prefer brand A of tea,

61% brand B, 60% brand C, 24% prefer A

and B, 35% B and C, 27% A and C, 5% liked

none of these brands.

To find : how many prefer all the three brands ?

solution : let n(u) = 100,

n(A) = 53, n(B) = 61, n(C) = 60 , n(A n B) = 24 ,

n(B n C) = 35 , n(A n C) = 27 and n(A u B u C)' = 5

we know, n(A u B u C) = n(u) - n(A u B u C)'

= 100 - 5 = 95

now using formula,

n(A u B u C) = n(A) + n(B) + n(C) - n(A u B) - n(B u C) - n(C u A) + n(A n B n C)

⇒95 = 53 + 61 + 60 - 24 - 35 - 27 + n(A n B n C)

⇒95 - 88 = n(A n B n C)

⇒n(A n B n C) = 7

Therefore 7 % respondents prefer all the three brands

Answer 2

$\huge \tt 7\%$