Suppose that a certain college class contains 46 students. Of these, 19 are seniors, 30 are mathematics 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 senior and a mathematics major? (b) Given that the student selected is a senior, what is the probability that she is also a mathematics major? Write your responses as fractions. (If necessary, consult a list of formulas.)

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