. A Television Survey A survey of 250 families in a housing society was taken to determine 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 antenna.
• 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 survey:
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?
Answers
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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