Question

In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is __.

Answer 1

n(A) = 40% of 10,000 = 4,000

n(B) = 20% of 10,000 = 2,000

n(C) = 10% of 10,000 = 1,000

n (A$\cap$B) = 5% of 10,000 = 500

n (B$\cap$C) = 3% of 10,000 = 300

n(C$\cap$A) = 4% of 10,000 = 400

n(A$\cap$B$\cap$C)= 2% of 10,000 = 200

Representation of data on Venn diagram

From the Venn diagram we observe that,

Number of families who buy A only = Number of families who buy A - Number of family who buy A and B - Number of family who buy A and C + Number of family who buy A, B and C

( since, we subtracted Number of family who buy A, B and C twice so, add it one time.)

= 4000 - 500 - 400 + 200 = 3300