document.write( "Question 1204187: Suppose a study of the faculty at U.S. medical schools revealed that 33% of the faculty were women and 67% were men. Of the female faculty, 33% were full/associate professors, 49% were assistant professors, and 18% 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? (Round your answer to two decimal places.) \n" ); document.write( "

Algebra.Com's Answer #840270 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Suppose a study of the faculty at U.S. medical schools revealed that 33% of the faculty were women and 67% were men.
\n" ); document.write( "Of the female faculty, 33% were full/associate professors, 49% were assistant professors, and 18% were instructors.
\n" ); document.write( "Of the male faculty, 51% were full/associate professors, 36% were assistant professors, and 13% were instructors.
\n" ); document.write( "If a faculty member at a U.S. medical school selected at random held the rank of full/associate professor,
\n" ); document.write( "what is the probability that the faculty member was female? (Round your answer to two decimal places.)
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document.write( "The probability under the problem's question is the conditional probability.\r\n" );
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document.write( "So, this probability is the ratio, where the denominator is the number of full or associate professors \r\n" );
document.write( "independently of the gender, while the numerator is the number of full or associate professors among women.\r\n" );
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document.write( "Based on it,  the numerator is 0.33*0.33;  the denominator is 0.33*0.33 + 0.67*0.51.\r\n" );
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document.write( "So, we write\r\n" );
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document.write( "    P =  = 0.24 (rounded as requested).    ANSWER\r\n" );
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