Suppose that a certain college class contains 55 students. Of these, 30 are juniors, 32 are physics majors, and 5are neither. A student is selected at random from the class.

(a) What is the probability that the student is both a junior and a physics major?

(b) Given that the student selected is a junior, what is the probability that he is also a physics major?

Write your responses as fractions.