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?
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