There was a survey in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

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Solution

Given survey data

n(A) = percentage of people read newspaper A = 42%

n(B) = percentage of people read newspaper B = 51%

n(C) = percentage of people read newspaper C = 68%

n(A∩B) = percentage of people read newspaper A and B = 30%

n(B∩C) = percentage of people read newspaper B and C = 28%

n(C∩A) = percentage of people read newspaper C and A = 36%

since, its given 8% people do not read any newspaper

percentage of people read newspaper = Total people - people don't read newspaper

n(AUBUC) = 100% - 8% = 92%

we know,

n(AUBUC) = ∑ n(A) - ∑ n(A∩B) + n(A∩B∩C)

92 = 42 + 51 + 68 - 30 - 28 - 36 + n(A∩B∩C)

92 = 161 - 94 + n(A∩B∩C)

92 = 67 + n(A∩B∩C)

n(A∩B∩C) = 92 - 67 = 25%

Percentage of people who read all the three newspapers = 25%

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