1. Suppose a study of the faculty at U.S. medical schools revealed that 38% of t

Question

1. Suppose a study of the faculty at U.S. medical schools revealed that 38% of the faculty were women and 62% were men. Of the female faculty, 33% were full/associate professors, 49% were assistant professors, and 18% were instructors. Of the male faculty, 52% were full/associate professors, 39% were assistant professors, and 9% 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? (Round your answer to two decimal places.)

Explanation / Answer

P(female) = 0.38

P(male) = 0.62

P(full/associate professors | female) = 0.33

P(full/associate professors | male) = 0.52

P(full/associate professors) = P(full/associate professors | female) * P(female) + P(full/associate professors | male) * P(male)

                                = 0.33 * 0.38 + 0.52 * 0.62

                                = 0.4478

P(femlae | full/associate professors) = P(full/associate professors | female) * P(female) / P(full/associate professors)

                                                          = 0.33 * 0.38 / 0.4478

                                                          = 0.28 (ans)

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