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?

Question

$\begin{array}{1 1} \large\frac{9}{13} \\ \large\frac{4}{13} \\ \large\frac{2}{13} \\ \large\frac{6}{13} \end{array} $