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

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.