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Q.3  Of the students in a college, it is known that  60^{o}/_{o}  reside in hostel and  40^{o}/_{o}  are day scholars (not residing in hostel). Previous year results report that  30^{o}/_{o}  of all students who reside in hostel attainA grade and  20^{o}/_{o}  of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A  grade, what is the probability that the student is a hostlier?

Answers (1)


H :   reside in hostel

D :  day scholars

A : students who attain grade A 




P(A|D)=\frac{20}{100}=\frac{2}{10}= \frac{1}{5}

By Bayes theorem :


                 P(H|A)=\frac{\frac{3}{5}\times \frac{3}{10}}{\frac{3}{5}\times \frac{3}{10}+\frac{2}{5}\times \frac{1}{5}}




Posted by

seema garhwal

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