Suppose that a certain college class contains 53 students. Of these, 31 are juniors, 29 are business majors, and 11 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a junior and a business major?
(b) Given that the student selected is a junior, what is the probability that he is also a business major? Write your responses as fractions