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

Question

1.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, 47% were assistant professors, and 21% 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.)

2.In a survey of 1012 adults aged 18 years and older conducted by a research company, it was found that gas prices have caused financial hardship for 65% of the respondents aged 18–49 years and 60% of those who are 50 years or older. There were 762 adults aged 18–49 years and 250 adults who were 50 years or older in the survey. If a respondent in the survey selected at random reported that he or she did not experience financial hardship from gas prices, what is the probability that he or she was an adult aged 18–49 years?(Round your answer to three decimal places.)

Explanation / Answer

1 .Probability of being a full/associate professor = 0.34*0.32+0.66*0.52 = 0.452

Given that a faculty is a full/associate professor, probability that faculty member is female = P(female|full/associate. professor) = P(full/associate|female).P(female)/P(full/associate professor) = 0.34*0.32/0.452 = 0.24

2. Probability of not experiencing financial hardship = 0.35*762/1012+0.4*250/1012 = 0.3623

P(Age between 18-49|No hardship) = P(No hardship|age between 18-49).P(age between 18-49)/P(no hardship) = 0.35*762/1012 / 0.3623 = 0.727

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