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.

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

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 neither Hindi nor English newspapers =1-P(H\cup E) 

                                                                                                             =1-(P(H)+P(E)-P(H\cap E))

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

                                                                                                             =1-\frac{4}{5}

                                                                                                              =\frac{1}{5}

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