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2.4. The following facts described the students who took my Bayesian statistics class in a recent year: 35% of the students were statistics grad students. 25% of the students were biostatistics grad students. 40% of the students were undergraduates or grad students from other depart ments. 60% of the statistics grad students were women. 75% of the biostatistics grad students were women. 40% of the students in other categories were women. * (a) You drew a student at random from my class list for that year. What is the probability that the student you drew is a woman? (b) Suppose that the student you drew was a woman. What is the probability that she was not a statistics grad student and not a biostatistics grad student, given that she was a woman?

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