Question

There are three brands of milk available for sale in a city - brand A, brand B and brand C. In a town of 10000 families, it was found that 40% families buy brand A, 20% buy brand B and 10% buy brand C. Also 5% families buy brands A and B, 3% buy B and C and 4% buy A and C. 2% families buy all the three brands.



Based on the above information answer the following :


i. Number of families which buy the milk of brand A only, is (a) 3030 (b) 3300 (c) 3003 (d) 4500


ii. Number of families which buy the milk of exactly two brands, are

(a) 600 (b) 990 (c) 60 (d) 6000


iii. What is the number of families which buy the milk of exactly one brand?

(a) 2500 (b) 5020 (c) 5200 (d) 2000


iv. Number of families which buy the milk of brands A and C but not B is

(a) 20 (b) 2000 (c) 400 (d) 200


v. What is the number of families which buy the milk of brands of at least one of A, B, C?

(a) 990 (b) 6000 (c) 9000 (d) 3000​

Answer 1

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

no. of people buy only A, only B & only C=1400+200+3300=4900

solution