Question

A survey show that $73$% of the indians like apples, where as $65$% like oranges. What percentage of indian like both apples and oranges?

Answer 1

Let the total number of people be $100x$

Given $73\%$ of total people like oranges $=\frac{73x}{100}\times 100=73x$

$65\%$ like oranges $=\frac{65}{100}\times 100x=65x$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$P(A\cap B)=P\left(A\right)+P\left(B\right)-P(A\cup B)$

$=73x+65x-100x$

$=38x$

Percentage of Indian like both apples and oranges $=\frac{38x}{100x}\times 100=38\%$