in survey of 60 people , it was found that 25 people read newspaper H , 26 read newpaper T , 26 read newspaper I , 9 read both H and I , 11 read both H and T , 8 read T and I , 3 read all these newspaper find

  1. the number of peoplewho read at least one of the new paper
  2. the number of people who read exactly one newpaper
  3. who read H but neither T nor I
  4. who read T and H but not I

plz replz as soon as possible , plz plz infinit

Let A be the set of people who read newspaper H.

Let B be the set of people who read newspaper T.

Let C be the set of people who read newspaper I.

Accordingly, n(A) = 25, n(B) = 26, and n(C) = 26

n(A ∩ C) = 9, n(A ∩ B) = 11, and n(B ∩ C) = 8

n(A ∩ B ∩ C) = 3

Let U be the set of people who took part in the survey.

(i) Accordingly,

n(A B C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

= 25 + 26 + 26 – 11 – 8 – 9 + 3

= 52

Hence, 52 people read at least one of the newspapers.

(ii) Let a be the number of people who read newspapers H and T only.

Let b denote the number of people who read newspapers I and H only.

Let c denote the number of people who read newspapers T and I only.

Let d denote the number of people who read all three newspapers.

Accordingly, d = n(A ∩ B ∩ C) = 3

Now, n(A ∩ B) = a + d

n(B ∩ C) = c + d

n(C ∩ A) = b + d

a + d + c + d + b + d = 11 + 8 + 9 = 28

a + b + c + d = 28 – 2d = 28 – 6 = 22

Hence, (52 – 22) = 30 people read exactly one newspaper

  • 5

1) n(H U T U I) = n(H) + n(T) + n(I) - n(H ∩ T) - n(T ∩ I) - n(I ∩ H) + n(H ∩ T ∩ I)

==> n(H U T U I) = 25 + 26 + 26 - 11 - 8 - 9 + 3 = 52

==> Total number of people read one or more papers is 52.

But given survey is done among 60 people; so 8 of them do not read any of the papers mentioned.

2) Only n(H U T) = n(H ∩ T) - n(H ∩ T ∩ I)

==> Only n(H U T) = 11 - 3 = 8

Similalry Only n(T U I) = 8 - 3 = 5

and Only n(I U H) = 9 - 3 = 6

3) Thus from the above, number of persons reading either two or three papers =

= Only n(H U T) + Only n(T U I) + Only n(I U H) + n(H ∩ T ∩ I) = 8 + 5 + 6 + 3 = 22

4) So number of people reading only one paper = Total number of people reading one or more papers - number reading two or three papers

= 52 - 22 = 30

Thus number of people reading only one paper = 30

Alternatively, you may try to solve in another method also:

i) Number of people read only H = Total H - (H ∩ T) - (H ∩ I) + (H ∩ T ∩ I)
= 25 - 11 - 9 + 3 = 8

ii) NUmber of people read only T = 26 - 11 - 8 + 3 = 10

iii) Number of people read only I = 26 - 8 - 9 + 3 = 12

So total reading only one paper = 8 + 10 + 12 = 30

However of the above two, the best one to solve is with VENN Diagram,

  • 35

thx u very much thx alot 

  • 1
lkkoowedhhqwnl
  • -7
Thank you
  • 1
Hope this would help

  • 6
Please find this answer

  • 2
b) In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all the three newspapers. Using the Venn diagram answer the following questions: i) No. of people who read atleast one newspaper. (1) ii) No. of people who read the newspaper H only.
 
  • 0
1) n(H U T U I) = n(H) + n(T) + n(I) - n(H ∩ T) - n(T ∩ I) - n(I ∩ H) + n(H ∩ T ∩ I) ==> n(H U T U I) = 25 + 26 + 26 - 11 - 8 - 9 + 3 = 52 ==> Total number of people read one or more papers is 52. But given survey is done among 60 people; so 8 of them do not read any of the papers mentioned. 2) Only n(H U T) = n(H ∩ T) - n(H ∩ T ∩ I) ==> Only n(H U T) = 11 - 3 = 8 Similalry Only n(T U I) = 8 - 3 = 5 and Only n(I U H) = 9 - 3 = 6 3) Thus from the above, number of persons reading either two or three papers = = Only n(H U T) + Only n(T U I) + Only n(I U H) + n(H ∩ T ∩ I) = 8 + 5 + 6 + 3 = 22 4) So number of people reading only one paper = Total number of people reading one or more papers - number reading two or three papers = 52 - 22 = 30 Thus number of people reading only one paper = 30 Alternatively, you may try to solve in another method also: i) Number of people read only H = Total H - (H ∩ T) - (H ∩ I) + (H ∩ T ∩ I) = 25 - 11 - 9 + 3 = 8 ii) NUmber of people read only T = 26 - 11 - 8 + 3 = 10 iii) Number of people read only I = 26 - 8 - 9 + 3 = 12 So total reading only one paper = 8 + 10 + 12 = 30 However of the above two, the best one to solve is with VENN Diagram, which you may try yourself.
  • 0
What are you looking for?