Question
Download Solution PDFIn a survey conducted over a group of people, it was found that 65% of them have a Facebook account, 40% of them have an Instagram account and 25% of them have a Twitter account. It was also concluded that 20% have an account on both Facebook and Instagram, 12% have an account on both Instagram and Twitter and 14% have an account on both Facebook and Twitter. If 8% of the people had an account on all the three websites, what percentage of the people do not have an account on any of the three websites?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLet,
⇒ n(F) = Percentage of people that have a Facebook account = 65%
⇒ n(I) = Percentage of people that have a Instagram account = 40%
⇒ n(T) = Percentage of people that have a Twitter account = 25%
Also,
⇒ n(F ∩ I) = Percentage of people that have an account on both Facebook & Instagram = 20%
⇒ n(F ∩ T) = Percentage of people that have an account on both Instagram & Twitter = 12%
⇒ n(I ∩ T) = Percentage of people that have an account on both Facebook & Twitter = 14%
⇒ n(F ∩ I ∩ T) = Percentage of people that have an account on all three websites = 8%
∵ According to the basic formula of Venn diagram for three elements,
⇒ n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)
⇒ n(F ∪ I ∪ T) = 65 + 40 + 25 – 20 – 12 – 14 + 8 = 92%
⇒ Percentage of people having an account on the three websites = 92%
∴ Percentage of people that do not have an account on any of the three websites = 100 – 92 = 8%Last updated on Jun 25, 2025
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