in a survey conducted among 200 mobile phone using families,it is found that 140 use Panasonic, 120 use Nokia and 143 use Siemens. 95 use both Panasonic and Nokia, 85 use both Nokia and Siemens and 93 use both Panasonic and Siemens. 70 family use mobile phones of all the three companies.
from the given data find the following:
1) how many families use mobile phones of only Siemens?
2) how many families use mobile phones of both Panasonic and Nokia but not Siemens?
3) how many families use mobile phones of exactly one company?
4) how many families use neither Panasonic nor Siemens?
5) how many families use none of the mobile phones?
Answers
67 families use mobile phones of exactly one company
Step-by-step explanation:
Total = 200
use Panasonic P = 140
use Nokia N = 120
use Siemens S= 143
use both Panasonic and Nokia = P ∩ N = 95
use both Nokia and Siemens = N ∩ S = 85
use both Panasonic and Siemens. P ∩ S = 93
use all the three P ∩ N ∩ S = 70
Use none = ?
Total = P + N + S - P ∩ N - N ∩ S - P ∩ S + P ∩ N ∩ S + None
=> 200 = 140 + 120 + 143 - 95 - 85 - 93 + 70 + None
=> None = 0
only Siemens = S - N ∩ S - P ∩ S + P ∩ N ∩ S
= 143 - 85 - 93 + 70
= 35
Panasonic and Nokia but not Siemens P ∩ N - P ∩ N ∩ S
= 95 - 70
= 25
Exactly one company = 22 + 10 + 35 = 67
use neither Panasonic nor Siemens = Only Nokia
120 - 95 - 85 + 70
= 10
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Answer:
Step-by-step explanation: