40% Students of a College Reside in Hostel and the Remaining Reside Outside. at the End of the Year, 50% of the Hostelers Got a Grade While from Outside Students, Only 30% Got a Grade in the Examination. - Mathematics

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40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ?

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Let E1 and E2 be the events that the student is a hosteller or an outside student, respectively and A be the event that the chosen student gets A grade.



P(A|E1)=P(Student getting A grade is a hosteller)=50%=0.5

P(A|E2)=P(Student getting A grade is an outside student)=30%=0.3

The probability that a randomly chosen student is a hosteller, given that he got A grade, is given by P(E1|A).

Using Bayes’ theorem, we get



`=0.20/0.38     `


Concept: Conditional Probability
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2014-2015 (March) Patna Set 2

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