Question

A Television Survey A survey of 250 families in a housing society was taken to determin
how they acquired their television service. The survey found that the families acquired their
television service through a cable service, through a satellite service (dish antenna), or by
using a regular antenna. Of the families surveyed:
155 used a cable service.
142 used a satellite service
80 used an antenna,
64 used both a cable service and a satellite service
26 used both a cable service and an antennas
55 used both a satellite service and an antenna
14 used all three methods to acquire their television service
How many of the families in the surveys
a used only a cable service to acquire their television service?
b. used only a satellite service to acquire their television service?
c did not use any of the three methods?​

Answer 1

Given : A survey of 250 families in a housing society was taken to determine  how they acquired their television service.

55 used a cable service.

142 used a satellite service

80 used an antenna,

64 used both a cable service and a satellite service

26 used both a cable service and an antennas

55 used both a satellite service and an antenna

14 used all three methods to acquire their television service

To Find : How many of the families in the surveys

a used only a cable service to acquire their television service?

b. used only a satellite service to acquire their television service?

c did not use any of the three methods?​

Solution:

cable service. C  = 155

satellite service S = 142

antenna,   A = 80

cable service and a satellite service  C ∩ S = 64

cable service and Antenna  C ∩ A = 26

satellite service  and Antenna  S ∩ A = 55

all three methods  C ∩ S ∩ A = 14

Only Cable service  = C - C ∩ S - C ∩ A +  C ∩ S ∩ A

= 155 - 64 - 26 + 14

= 169 - 90

= 79

only a satellite service = S  - C ∩ S - S ∩ A +  C ∩ S ∩ A

= 142 - 64  - 55 + 14

= 156 - 119

= 37

T = C + S + A - C ∩ S - C ∩ A -  S ∩ A +  C ∩ S ∩ A + None

=> 250 = 155 + 142 + 80  - 64 -26 - 55 + 14 + None

=> 250 = 246 + None

=> None = 4

4 did not use any of the three methods

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