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3. 24 the following facts described the students who took my...

# Question: 24 the following facts described the students who took my...

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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 departments.

• 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?