1. In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having atleast one among cable -TV and VCR?
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By: anil on 05 May 2019 02.33 am
Let the distribution of people having cable TV and VCR be as given in the diagram above.
Hence, $$a+c =frac{2}{3}$$
$$b+c=frac{1}{5}$$
and $$c=frac{1}{10}$$ We need to find $$a+b+c=?$$
This equals $$(a+b)+(b+c)-c = frac{2}{3}+frac{1}{5}-frac{1}{10}$$
Which equals $$frac{20+6-3}{30}=frac{23}{30}$$
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Hence, $$a+c =frac{2}{3}$$
$$b+c=frac{1}{5}$$
and $$c=frac{1}{10}$$ We need to find $$a+b+c=?$$
This equals $$(a+b)+(b+c)-c = frac{2}{3}+frac{1}{5}-frac{1}{10}$$
Which equals $$frac{20+6-3}{30}=frac{23}{30}$$