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In 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?

In 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? Correct Answer 8%

Let,

⇒ 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%

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