Of the students in a college, it is known that 60% reside in hostel and 40% are 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 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?

Given: let E1 be the event that student is a hostler, E2 be the event that student is a day scholar and A be the event of getting A grade.



Also P(A|E1) = P (students who attain A grade reside in hostel) = 30% = 0.3

And P(A|E2) = P (students who attain A grade is day scholar) = 20% = 0.2

Now the probability of students who reside in hostel, being given he attain A grade, is P(E1|A).

By using bayes’ theorem, we have: