Question
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 residue in hostel attain A grade and 20% of day scholars attain A grade in their annua! 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?
Solution
Let E1, E2, E be the events
E1 : ‘A student is residing in hostel’
E2 : ‘A student is day scholar’,
E : ‘A student gets A grade,’
Now, 
Required probability = 
