Question
Mon February 25, 2013 By:

# in a town of 10000 families it was found that 40%families buy newspaper a,20% buy newspaper b and 10%buy newspaper c.5% families buy a and b.3% buy b and c and 4% buy a and c.if 2% buy all newspapers.find the number of families that buy a only b only none of a,b and c

Mon February 25, 2013
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  B) = 5% of 10,000 = 500
n (B  C) = 3% of 10,000 = 300
n(C  A) = 4% of 10,000 = 400,
n(A  B  C) = 2% of 10,000 = 200
We want to find n(A  only) = n(A) Â– [n(A  B) + n(A  C)] + n(A  B C)=
n(A  only) = 4000 Â– [500 + 400] + 200 = 4000 Â– 700 = 3300

Similarly, n(B only) = n(B) Â– [n(A  B) + n(B C)] + n(A  B C)
n(B only)  = 2000 - [500+300]+200 = 1400

n(none of A, B and C) = 10,000 - [n(A)+n(B) + n(C) - n (A  B) - n(B C) - n (C A) + n(AB C)]
n(none of A, B and C) = 10,000 - [4000+2000+1000 - 500-300-400 + 200]
n(none of A, B and C) = 4000
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