# Q. 15 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 three newspapers. Find:(i) the number of people who read at least one of the newspapers.(ii) the number of people who read exactly one newspaper.

D Divya Prakash Singh

n(H) = 25

n(T) = 26

n(I) = 26

n(H $\cap$ I) = 9

n( T $\cap$ I ) = 8

n( H $\cap$ T ) = 11

n(H $\cap$ T $\cap$ I ) = 3

the number of people who read at least one of the newspapers = n(H$\cup$T$\cup$I) = n(H) + n(T) + n(I) - n(H $\cap$ I) -  n( T $\cap$ I ) - n( H $\cap$ T ) + n(H $\cap$ T $\cap$ I )

= 25 + 26 + 26 - 9 - 8 - 11 + 3

= 52

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

(ii) number of people who read exactly one newspaper =

the number of people who read at least one of the newspapers -  n(H $\cap$ I) -  n( T $\cap$ I ) - n( H $\cap$ T ) + 2 n(H $\cap$ T $\cap$ I )

=  52 - 9- 8 -11 + 6

=   30

Hence, 30 number of people who read exactly one newspaper .

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