Suppose that a certain college class contains 58 students. Of these,34 are sophomores, 32 are chemistry majors, and8 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 chemistry major?
(b) Given that the student selected is a sophomore, what is the probability that she is also a chemistry major?
Write your responses as fractions.