Incoming students at a certain school take a mathematics placement exam. The possible scores are 1, 2, 3, and 4. From past experience, the school knows that if a particular student's score is {1,2,3,4}, then the student will become a mathematics major with probability 3. Suppose that the incoming class had the following scores: 10% of the students scored a 1, 20% of the students scored a 2, 60% scored a 3, and 10% scored a 4. (a) What is the probability that a randomly selected student from the incoming class will become a mathematics major? (b) Suppose a randomly selected student from the incoming class turns out to be a mathematics major. What is the probability that he or she scored a 4 on the placement exam?