Please see the attached file for full problem description.
Suppose that a certain college class contains students. Of these, are sophomores, are chemistry majors, and 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. Suppose that we are given the additional information that the student selected is a sophomore. What is the probability that she is also a chemistry major?
Give your answers as exact fractions.