Suppose a study of the faculty at U.S. medical schools revealed that 34% of the

Question

Suppose a study of the faculty at U.S. medical schools revealed that 34% of the faculty were women and 66% were men. Of the female faculty, 32% were full/associate professors, 49% were assistant professors, and 19% were instructors. Of the male faculty, 54% were full/associate professors, 36% were assistant professors, and 10% 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

Answer:

Suppose a study of the faculty at U.S. medical schools revealed that 34% of the faculty were women and 66% were men. Of the female faculty, 32% were full/associate professors, 49% were assistant professors, and 19% were instructors. Of the male faculty, 54% were full/associate professors, 36% were assistant professors, and 10% 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.)

P( W)=0.34      P(FP/W)=0.32     P(AP/W)=0.49    P(FP/W)=0.19  

P(M)=0.66   P(FP/M)=0.54     P(AP/M)=0.36    P(FP/M)=0.10  

P(W/FP) = P(FP/W)* P( W) / (P(FP/W)* P( W)+ P(FP/M)* P( M) )

=0.32*0.34/ (0.32*0.34+0.54*0.66)

=0.233877902

=0.23   ( TWO DECIMALS).

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