[10 pts.] a.) Suppose the fraction of undergraduate students who smoke is 15% and the fraction of graduate students who smoke is 30%. If one-fifth of the college students are graduate students and the rest are undergrad- uates, what is the probability that a student who smokes is a graduate student. b) Suppose 30% of the graduate students live in a dorm but only 10% of the undergraduate students live in a dorm. If a student smokes and lives in the dorm, are they more likely to be a graduate or undergraduate student? (You may assume independence between the two relevant attributes.)