In a town of 10,000 families, it was found that 40% of families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy newspapers A and B, 3% families buy newspapers B and C, 4% families buy newspapers A and C. If 2% of the families buy all the three newspapers, find the number of families which buy (i) A only (ii) None of A, B and C (iii) at least one of A, B or C (iv) Exactly one of A, B or C.
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Answer
Number of families=10000
n(A)=
100
40×10000
=4000
n(B)=
100
20×10000
=2000
n(C)=
100
10×10000
=1000
n(A∩B)=
100
5×10000
=500
n(A∩C)=
100
4×10000
=400
n(B∩C)=
100
3×10000
=300
n(A∩B∩C)=
100
2×10000
=200
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