Suppose that a certain college class contains 52 students. Of these, 21 are sophomores, 32 are mathematics majors, and 8 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a sophomore and a mathematics major? (b) Given that the student selected is a sophomore, what is the probability that he is also a mathematics major? Write your responses as fractions. (If necessary, consult a list of formulas.) (a) (b)