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1. A market research team interviews 160 students,asking each of
them wheather he reads anyof all of the magazine: A,India Today;B
Business India; C, Today. The team returns the
following data:
Category Number Category Number
A 60 AC 20
B 50 AB 30
C 50 ABC 10
AC 30
Are the returns consistent?
Ans- Given,
Total no of students, n(U)=160
No of students reading India Today,n(A)=60
No of students reading Business India,n(B)=50
No of students reading Today,n(C)=50
n(AC)=30
n(BC)=20
n(AB)=30
n(ABC)=10
Hence, n(AUBUC)=n(A)+n(B)+n(C)-n(AB)-n(BC)-n(AC)+n(AUBUC)
=60+50+50-30-20-30+10=90
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Hence no of items which had exactly 1
defect,n(SUW)-n(sW)=34-10=24
3. In a certain examination 75 % pass in group A and 82 % in
group B and 15% fail in both thegroups. Find out what percent are
pass in the examination?
Ans: In group A 75 % passed,hence percentage of students faied
in group A , n(Af)=25%
In group B 82% passed,hence percentage of student failed in
group B, n(Bf)= 18%
Now given that n(AfBf)= 15
Hence,n(AfUBf)= n(Af) + n(Bf) - n(AfBf)= 25+18-15=28
So 28% failed in atleast 1 subject. So 100-28= 72% passed in the
examination.
4. In a recent survey of 400 students in a school it was found
out that 100 students readsmagazine A and 150 read magazine B , 75
read both the magazines. Find out how many read
eirher magazine.
Ans: Given, no of students reading magazine A,n(A)=100
no of students reading magazine B,n(B)=150
no of students reading both the magazines, n(AB)=75
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n(AUB) = n(A) + n(B) n(AB)=100+150-75=175
Hence no of students reading either magazines=n(AUB)-n(AB)=
175-75=100
5. In a survey students in a music school, the number of
students learning one or moreinstruments: Tabla,Veena, Guitar were
interviwed. The data is given below:
Category Number Category Number
T 25 TV 10
V 32 TG 12
G 43 VG 4
TGV 3
(i) How many students were learning none of these three musical
instruments?(ii) How many students were learning only the
guitar?
Ans: Given,no of students learning tabla,n(T)=25
No of students learning veena,n(V)=32
No of students learning guitar,n(G)=43
And,n(TV)=10
n(TG)=12
n(VG)=4
n(TVG)=3
n(TUGUV)=n(T)+n(G)+n(V)- n(TV)-
n(TG)-n(VG)+n(TVG)=25+32+43-10-12-4+3=77
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(i)Hence no of students which were not learning any of these
instruments=100-77=23
(ii)no of students learning only
guitar,n(G)-n(GV)-n(GTVc)=43-4-9=30
