3. In a survey of market, it is noted that 300 families randomly selected in a city, 142 buy Lipton tea and 139 buy Brookbond tea and 70 buy both type of tea. Find out the number of families who buy (i) at least one brand of tea (ii) exactly one of these brands (iii) none of these brands.
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Answer:
(i) 211 families (ii) 141 families (iii) 89 families
Step-by-step explanation:
Total families = 300
Families that buy lipton tea, n(A) = 142
Families that buy Brookbond tea, n(B) = 139
Families that buy both the teas, n(A ∩ B) = 70
(i) at least one brand = n(A∪B)
n(A∪B) = n(A) + n(B) - n(A∩B)
= 142 + 139 - 70
= 211 families
(ii) exactly one of these brands
= Families buying at least one brand - families buying both brands
n(A) + n(B) - 2n(A ∩ B) = 142 +139 - 2*70
= 141 families
(iii) none of these brands
Total - n(A∪B)
= 300 - 211
= 89 families
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