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Of the students in a college, it is known that 60% reside in hostel and 40% day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day cholars 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 hosteler?

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The correct Answer is:
N/a
Let `E_(1)=` event of selecting a student reside in hostel,
`E_(2)=` event of selecting a student not residing in hostel,
`E=` event that the student has A grade.
`:.P(E_(1))=60/100,P(E_(2))=40/100`
`P(E//E_(1))=30/100,P(E//E_(2))=20/100`
`:.P(E_(1)//E)=` probability that the selected student has A grade when he reside in hostel
`=(P(E_(1)).P(E//E_(1)))/(P(E_(1)).P(E//E_(1)+P(E_(2)).P(E//E_(2)))`
`=(60/100xx30/100)/(60/100xx30/100+40/100xx20/100)`
`=18/(18+8)=9/13`
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