Suppose a study of the faculty at U.S. medical schools revealed that 37% of the faculty were women and 63% were men. Of the female faculty, 31% were full/associate professors, 46% were assistant professors, and 23% were instructors. Of the male faculty, 51% were full/associate professors, 36% were assistant professors, and 13% were instructors. If a faculty member at a U.S. medical school selected at random held the rank of full/associate professor, what is the probability that the faculty member was female?
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