Q. 16    In a hostel, 60\; ^{o}/_{o} of the students read Hindi newspaper, 40\; ^{o}/_{o}  read English newspaper and 20\; ^{o}/_{o}  read both Hindi and English newspapers. A student is selected at random.

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

Answers (1)

H : 60\; ^{o}/_{o}  of the students read Hindi newspaper,

E : 40\; ^{o}/_{o} read English newspaper       and  

 H \cap E :  20\; ^{o}/_{o} read both Hindi and English newspapers.

P(H)=\frac{60}{100}=\frac{6}{10}=\frac{3}{5}

P(E)=\frac{40}{100}=\frac{4}{10}=\frac{2}{5}

P(H\cap E)=\frac{20}{100}=\frac{2}{10}=\frac{1}{5}

The probability that she reads English newspape if she reads Hindi newspaper =P(E|H)

                                                                                  P(E|H)=\frac{P(E\cap H)}{P(H)}

                                                                                  P(E|H)=\frac{\frac{1}{5}}{\frac{3}{5}}

                                                                                P(E|H)=\frac{1}{3}

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