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.

Answers (1)

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\cupT\cupI) = 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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