Question

In a hostel, 60% of the students read Hindi newspaper 40% read English newspaper and 20% read both read both Hindi and English newspapers. A student is selected at random
IF he/she reads Hindi newspaper, find the probability that she reads English newspaper.

Answer 1

Let H: set of students reading Hindi newspaper and E: set of students reading English newspaper.
Let $n\left(S\right)=100then,n\left(H\right)=60n\left(E\right)=40andn(H\cap E)=20\therefore P\left(H\right)=\frac{n\left(H\right)}{n(SH}=\frac{60}{100}=\frac{3}{5},P\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}=\frac{40}{100}=\frac{2}{5}andP(H\cap E)=\frac{n(H\cap E)}{n\left(S\right)}==\frac{20}{100}=\frac{1}{5}$
Required probability = P (student reads Hindi newspaper when it is given that reads English newspaper)
$\therefore P\left(\frac{H}{E}\right)=\frac{P(H\cap E)}{P\left(E\right)}=\frac{\frac{1}{5}}{\frac{2}{5}}=\frac{1}{2}$