Question

In a locality two-thirds of the people have cable TV one-fifth have Dish TV and one-tenth have both What is the fraction of people having either cable TV or Dish TV?

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{4}{5}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A $\frac{2}{3}$

Fraction of people who watch cable only $=(\frac{2}{3}-\frac{1}{10})=\frac{17}{30}$
Fraction of people who watch Dish TV only $=(\frac{1}{5}-\frac{1}{10})=\frac{1}{10}$
$\therefore$ Fraction of people who watch either cable of Dish TV $=\frac{17}{30}+\frac{1}{10}=\frac{20}{30}=\frac{2}{3}$