Question

(v) In a survey of 60 people it was found that 25 people read newspaper A, 26 read
newspaper B, 26 read newspaper C, 9 read both A and C, 11 read both A and B. 8
read both B and C and 3 read all. Find
(a) number of people who read at least one newspaper
(b) the number of people who read exactly one newspaper​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{blue}{blue}{Answer}}$

Step-by-step explanation:

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.

Given

n(A)=25,n(B)=26, and n(C)=26

n(A∩C)=9,n(A∩B)=11, and (B∩C)=8

n(A∩B∩C)=3

Let

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

(i) 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 newspaper.

(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 newspaper T and I only.

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

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.

HOPE IT HELPS YOU FRIEND...☺

》》Arnav☆

Answer 2

Answer:

$\huge\boxed{\fcolorbox{green}{green}{Answer}}$

Step-by-step explanation:

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.

Given

n(A)=25,n(B)=26, and n(C)=26

n(A∩C)=9,n(A∩B)=11, and (B∩C)=8

n(A∩B∩C)=3

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

(i) 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 newspaper.

(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 newspaper T and I only.

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

According to,

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.

HOPE IT HELPS YOU FRIEND...

》》Ⱥʀɲɑѵ☆