14.Probability
easy

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 Find the probability that she reads neither Hindi nor English newspapers.

A

$\frac{1}{5}$

B

$\frac{1}{5}$

C

$\frac{1}{5}$

D

$\frac{1}{5}$

Solution

Let $H$ denote the students who read Hindi newspaper and $E$ denote the students who read English newspaper.

It is given that, $\mathrm P(H)=60 \%=\frac{60}{100}=\frac{3}{5}$

$\mathrm{P}(\mathrm{E})=40 \%=\frac{40}{100}=\frac{2}{5}$

$P(H \cap E)=20 \%=\frac{20}{100}=\frac{1}{5}$

Probability that a student reads Hindi and English newspaper is,

$\mathrm{P}(\mathrm{H} \cup \mathrm{E})^{\prime}=1-\mathrm{P}(\mathrm{H} \cup \mathrm{E})$

$=1-\{\mathrm{P}(\mathrm{H})+\mathrm{P}(\mathrm{E})-\mathrm{P}(\mathrm{H} \cap \mathrm{E})\}$

$=1-\left(\frac{3}{5}+\frac{2}{5}-\frac{1}{5}\right)$

$=1-\frac{4}{5}$

$=\frac{1}{5}$

Standard 11
Mathematics

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