in a survey of 80 peopleit was found that 25 read danik jagran 26 read amar ujala 26 read hindustan 9 read both amar ujala and danik jagran 11 read hindustan amar ujala 8 read danik jagran and hindustan and 3 read all three newspapers find how many read (1) none of them (2) at least one news paper (3) exactly one news paper
Answers
Given : survey of 80 people who read danik jagran , amar ujala and hindustan
To find : how many read (1) none of them (2) at least one news paper (3) exactly one news paper
Solution:
Total People = 80
read danik jagran D = 25
read amar ujala A = 26
read hindustan H = 26
read both amar ujala and danik jagran A ∩ D = 9
read hindustan amar ujala A ∩ H = 11
read danik jagran and hindustan D ∩ H = 8
read all three newspapers A ∩ D ∩ H = 3
Read none = ?
T = D + A + H - A ∩ D - A ∩ H - D ∩ H + A ∩ D ∩ H + none
=> 80 = 25 + 26 + 26 - 9 - 11 - 8 + 3 + None
=> None = 28
28 Read None of Them
at least one news paper = total - Read none
= 80 - 28
= 52
52 read atleast one news paper
only danik jagran = D - A ∩ D - D ∩ H + A ∩ D ∩ H
= 25 - 9 - 8 + 3
= 11
only Amar Ujala = A - A ∩ D - A ∩ H + A ∩ D ∩ H
= 26 - 9 - 11 + 3
= 9
only hindustan = H - H ∩ D - A ∩ H + A ∩ D ∩ H
= 26 - 8 - 11 + 3
= 10
Read exactly one news paper = 11 + 9 + 10 = 30
30 Read exactly one news paper
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