Question

In a survey of 300 android mobile users who make video calls, 75 people said they use Viber, 45 use Skype, and 30 people use both. The number of persons who use neither Viber nor Skype is __.

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Answer

Given the data from the survey:

  • Total surveyed mobile users, ( n(U) = 300 )
  • Users of Viber, ( n(V) = 75 )
  • Users of Skype, ( n(S) = 45 )
  • Users of both Viber and Skype, ( n(V \cap S) = 30 )

To find the number of users who use neither Viber nor Skype, we use the principle of inclusion-exclusion for counting:

  1. Inclusion-Exclusion Formula: $$ n(V \cup S) = n(V) + n(S) - n(V \cap S) $$ Substituting the given values: $$ n(V \cup S) = 75 + 45 - 30 = 90 $$

  2. The number of persons who use neither Viber nor Skype is: $$ n(U) - n(V \cup S) $$ Thus: $$ n(V^I \cap S^I) = n(U) - n(V \cup S) = 300 - 90 = 210 $$

Therefore, the number of persons who use neither Viber nor Skype is 210.


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