JEE Main 2019 — Probability Question with Solution

Let $n\left(A\right)$ and $n\left(B\right)$ be the percentage of population in a city who read newspaper $A$ and $B$ respectively.

Therefore, $n\left(A\right)=25,$ $n\left(B\right)=20$ and $n\left(A\cap B\right)=8$

Now, we know that

$n\left(A\cap \overline{B}\right)=n\left(A\right)-n\left(A\cap B\right)$

$\Rightarrow n\left(A\cap \overline{B}\right)=25-8$

$\Rightarrow n\left(A\cap \overline{B}\right)=17$

And,

$n\left(\overline{A}\cap B\right)=n\left(B\right)-n\left(A\cap B\right)$

$\Rightarrow n\left(\overline{A}\cap B\right)=20-8$

$\Rightarrow n\left(\overline{A}\cap B\right)=12$

Therefore, percentage of those who read advertisements is

$=30\%$ of $n\left(A\cap \overline{B}\right)+40\%$ of $n\left(B\cap \overline{A}\right)+50\%$ of $n\left(A\cap B\right)$

$=\frac{30}{100}\times 17+\frac{40}{100}\times 12+\frac{50}{100}\times 8$

$=\frac{1390}{100}$

Total persons who look into advertisement $=13.9\%$