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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 attain $A$ 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?

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best_answer

H : reside in hostel

D : day scholars

A : students who attain grade A

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

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

$P(A|H)=\frac{30}{100}=\frac{3}{10}$

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

By Bayes theorem :

$P(H|A)=\frac{P(H).P(A|H)}{P(H).P(A|H)+P(D).P(A|D)}$

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

$P(H|A)=\frac{\frac{9}{50}}{\frac{9}{50}+\frac{2}{25}}$

$P(H|A)=\frac{\frac{9}{50}}{\frac{13}{50}}$

$P(H|A)=\frac{9}{13}$

Posted by

seema garhwal

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