An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Find

Question

An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Find
(i) how many use only Radio?

(ii) how many use only Television?

(iii) how many use Television and magazine but not radio?

Philoid · Accepted Answer

Lets Let T,R and M are the people who use Television, Radio and Magazines respectively.

Number of people who use Television n(T) = 115

Number of people who use Radio n(R) = 110

Number of people who use Magazine n(M) = 130

Number of people who use Television and Magazines, n(T ∩ M) = 85

Number of people who use Television and Radio, n(T ∩ R) = 75

Number of people who use Radio and Magazine, n(R ∩ M) = 95

Number of people who use all the three n(T ∩ R ∩ M) = 70

Here we have to find,

Number of People using Radio only = n(R’)

Number of People using Television only = n(T’)

Number of People using Television & magazine but not radio = n(T∩M∩R’)

Using the data given we can draw a Venn diagram,

So from the Venn diagram it’s clear that

(i) Number of People using Radio only = R’ = 10

(ii) Number of people using television only = T’ = 25

(iii) Number of People using Television & magazine but not radio = n(T∩M∩R’) = 15