In a survey of 100 people, 65 reads kanthipur or ghorkgapatra,10 reads Himalayan times only ..how many people didn't reads 3 newspapers
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In a certain city two newspapers A and B are published. It is known that 25% of the city population reads A and 20% of the population reads B. 8% of the population reads both A and B. It is known that 30% of those who read A but not B look into advertisements and 40% of those who read B but not A look advertisements while 50% of those who read both A and B look into advertisements . What is the percentage of the population who reads an advertisement?
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ANSWER
Let P(A) and P(B) denote the precentage of city population who reda newspapers A and B.
Then from given data ,we have
P(A)=25%==
4
1
,P(B)=20%==
5
1
.
P(A∩B)=8%=
25
2
.
∴ Percentage of those who read A but not B P(A∩
B
ˉ
)=P(A)−P(A∩B) [see theorem 2 & 3] =
4
1
−
25
2
=
100
17
=17%
Similarly,P(
A
ˉ
∩B)=P(B)−P(A∩B) =
5
1
−
25
2
=
25
3
=12%
If P(C) denotes the percentage of those who look into advertisement , then from the given data we obtain P(C)30%ofP(A∩
B
ˉ
)+40% of
P(A∩
B
ˉ
)+50ofP(A∩B)
=
10
3
×
100
17
+
5
2
×
25
3
+
2
1
×
25
2
=
1000
51+48+40
=
1000
139
=13.9%.
Thus the percentage of population who read an advertisement is 13.9%
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