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Question

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

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Solution

## Let E1 : the event that the student is residing in hostel and E2 : the event that the student is not residing in the hostel. Let E: a student attains A grade, Then, E1 and E2 are mutually exclusive and exhaustive. Moreoever, PE1 =60%= 60100=35 and PE2 =40%=40100=25 Then, P(EE1)=30 and P(EE2)=20 By using Baye's theorem, we obtain P(EE1)=P(EE1)P(E1)P(EE1)P(E1)+P(EE2)P(E2)=310×35310×35+210×25=99+4=913

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