At a university, 30% of the students live in the hostel and 20% are scholarship holders. Among scholarship holders, 40% live in the hostel.
a. (i) Find the probability that a randomly chosen student both lives in the hostel and is a scholarship holder.
b. (ii) Determine the probability that a scholarship holder does not live in the hostel.
c. (iii) Calculate the probability that a student lives in the hostel given that the student is not a scholarship holder.