Solution:

Let represent the event that the student is a hostler, represent the event that the student is a day scholar, and represent the event that the student receives an A grade.

Then

And

Also students who attain A grade reside in hostel)

And (students who attain A grade is day scholar) =

The likelihood that students who live in hostels will receive an A grade is now .

By using Bayes’ theorem, we have:

We can acquire the values by substituting them.