Suppose that a certain college class contains 35 students. Of these, 22are seniors, 16 are mathematics majors, and 5 are neither. A student is selected at random from the class.

(a) What is the probability that the student is both a senior and a mathematics major?

(b) Given that the student selected is a mathematics major, what is the probability that she is also a senior?

Write your responses as fractions.