 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says of the students in a college it is known that 60% reside in hostel and 40% are day scholars. 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 hostler? Now in this question we will use Bayes theorem. So according to this theorem if even E2 so on EN are N non-empty events which constitute a partition of sample space S that is even E2 so on EN are pairwise disjoint and even union E2 union so on union EN is equal to S and A is any event of non-zero probability then probability of EI upon A is equal to probability of EI into probability of A upon EI over sigma probability of EJ into probability of A upon EJ J varying from 1 to N for any I 1 to N. So this is the key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. Now according to the given question of the students in a college it is known that 60% reside in hostel and 40% are the scholars. So let even be the event that the students reside in hostel E2 be the event that the student is a day scholar. Therefore probability of E1 is equal to 60% which is equal to 60 over 100 and this is again equal to 0.6 and probability of E2 is equal to 40% and this is equal to 40 over 100 and this is again equal to 0.4. Now again according to the given question 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 the annual examination. So let A be the event of getting A grade. So probability of A upon E1 is equal to probability that the student getting an A grade is a hostel and this is equal to 30% which is equal to 0.3. Now probability of A upon E2 probability that the student getting an A grade is a day scholar and this is equal to 20% which is equal to 0.2. Now again according to the question at the end of the year one student is chosen at random from the college and he has an A grade we have to find the probability that the student is a hostel. So the probability that the hostel is getting an A grade and this is given by probability of even upon A so by using this term we have probability of even upon A is equal to that is the probability of the even even given that even A has occurred is equal to probability of even into probability of A upon E1 over probability of even into probability of A upon E1 plus probability of E2 into probability of A upon E2. Now we have probability of even is equal to 0.6 probability of E2 is equal to 0.4 probability of A upon even is equal to 0.3 and probability of A upon E2 is equal to 0.2. So on substituting these values we have probability of even upon upon A is equal to 0.6 into 0.3 over 0.6 into 0.3 plus 0.4 into 0.2 and this is equal to 0.18 over 0.18 plus 0.08 and this is again equal to 0.18 over 0.26 this is again equal to 18 over 0.26 which is equal to 9 over 13 so the probability that the hostel is getting an A grade is 9 over 13. So this completes our session I hope the solution is clear to you by and have a nice day.