Question:

Of the 62 male and 59 female doctoral candidates (G2 and up] at the Department of Government, 44 are studying comparative politics exclusively, 14 are studying political methodology exclusively, and 13 study both comparative politics and methodology. (Assume for simplicity that there is no one that studies method— ology and another subfield, e.g. no one studies both American politics and methodology.) By gender, the breakdown of PhD. candidates in the department is as follows:

1. Now, suppose the Department has just instituted a graduate student mentoring program. Suppose you’re an incoming G1 and you have been assigned randomly a mentor from the candidate ranks. At this point, you do not know if your graduate student mentor is a woman or man.

1. What is the probability that your mentor studies comparative politics and methods? (Hint: It is often helpful to draw Venn diagrams for problems like these.)
2. What is the probability your mentor studies comparative politics or methods or both?

B) Now, suppose you’ve just received your mentor assignment from Thom wall and you have been paired randomly with a woman mentor.

1. Given that your mentor is a woman, what is the probability that she studies comparative politics and methods?
2. "That is the probability that she studies comparative politics or methods or both?

C) Suppose you have been paired with a woman mentor who you know studies at least comparative politics. Knowing that, what is the probability that she studies both comparative politics and methods?

D) Suppose instead that you have been paired with a. woman mentor who studies methods, and you have no idea whether she studies comparative politics. Given this information, what is the probability that she studies both methods and comparative politics? Explain intuitively why this answer is different from the answer in part C.

E) Suppose that you request a mentor who studies comparative politics, and Thom randomly assigns one to you from among all male and female comparativists. Is receiving a woman mentor independent of receiving a mentor with interests in methodology? Use a mathematical explanation to answer why or why not.

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