Question

In a hostel, 60% of the students read Hindi newspaper, 40%read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random:
(i) Find the probability that she reads neither Hindi or English newspaper.
(ii) If she reads Hindi newspaper, find the probability that she reads English newspaper.
(iii) If she reads English newspaper. Find the probability that she reads Hindi newspaper.

Answer 1

For Hindi=H

English=E

Given $P\left(H\right)=60$ % $=0.6$

$P\left(E\right)=40$ % $=0.4$

$P(H\bigcap E)$=20=0.2$

(i) Neither reads Hindi nor English

$P(H^{\prime }\bigcap E^{\prime })=1-P(H\bigcup E)$

$=1-[P\left(H\right)+P\left(E\right)-P(H\bigcap E)]$

$=1-[0.6+0.4-0.2]$

$=1-0.8$

$=0.2$

(ii) Reads English, if reads Hindi

$\therefore P\left(E/H\right)=\frac{P(H\bigcap E)}{P\left(H\right)}$

$=\frac{0.2}{0.6}=\frac{1}{3}$

(iii) Reads Hindi, given that reads English

$P\left(H/E\right)=\frac{P(H\bigcap E)}{P\left(E\right)}=\frac{0.2}{0.4}$

$=0.5$