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Home » In a hostel, of the students read Hindi newspaper, read English newspaper and read both Hindi and English newspapers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English newspapers. (b) If she reads Hindi newspaper, find the probability that she reads English newspaper. (c) If she reads English newspaper, find the probability that she reads Hindi newspaper
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.
(a) Find the probability that she reads neither Hindi nor English newspapers.
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper
CBSE | Maths | NCERT | Probability
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.
(a) Find the probability that she reads neither Hindi nor English newspapers.
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper

Given:

The letters H and E stand for the number of students who read the Hindi newspaper and the English daily, respectively.

Hence, \mathrm{P}(\mathrm{H})= Probability of students who read Hindi newspaper =60 / 100=3 / 5

P(E)= Probability of students who read English newspaper =40 / 100=2 / 5

P(H \cap E)= Probability of students who read Hindi and English both newspaper =20 / 100

=1 / 5

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

P (neither H nor E)

P( neither H nor E)=P\left(H^{\prime} \cap E^{\prime}\right)

As, \left{\mathrm{H}^{\prime} \cap \mathrm{E}^{\prime}=(\mathrm{H} \cup \mathrm{E})^{\prime}\right}

\&

\Rightarrow P (neither A nor B)=P\left((H \cup E)^{\prime}\right)

=1-P(H \cup 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-\left[\frac{4}{5}\right]=\frac{1}{5}

(b) If she reads a Hindi newspaper, calculate the likelihood that she also reads an English daily..

P(E \mid H)= Hindi newspaper reading has already occurred and the probability that she reads English newspaper is to find.

As we know P(E \mid H)=\frac{P(H \cap E)}{P(H)}

\Rightarrow \mathrm{P}(\mathrm{E} \mid \mathrm{H})=\frac{\frac{1}{3}}{\frac{3}{5}}=\frac{1}{5} \times \frac{5}{3}

\Rightarrow \mathrm{P}(\mathrm{E} \mid \mathrm{H})=1 / 3

(c) If she reads English newspaper, find the probability that she reads Hindi newspaper.

P(\mathrm{H} \mid \mathrm{E})= English newspaper reading has already occurred and the probability that she reads Hindi newspaper is to find.

As we know P(H \mid E)=\frac{P(H \cap E)}{P(E)}

\Rightarrow P(\mathrm{H} \mid \mathrm{E})=\frac{\frac{1}{2}}{\frac{5}{5}}=\frac{1}{5} \times \frac{5}{2}

\Rightarrow \mathrm{P}(\mathrm{H} \mid \mathrm{E})=1 / 2

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