For the biological sciences and health sciences faculty combined, \(\frac{1}{3}\) of the female and \(\frac{2}{9}\) of the male faculty members are tenured professors. What
fraction of all the faculty members in those two fields combined are tenured professors?


Give Your Answer in Fraction:





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Sandy
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I took 3 mins 20 s to do this question.

Why can't we do the following:

#females bio: .05*200 = 10
#males bio: .16*250=20
likewise,
#females health: 40
# males health: 20

#tenured females in bio & health: (5)*1/3 = 16.667
#tenured males in bio & health: (20)*(2/9) = 4.444
#tenured females: (1/3)*200 = 66.66
#tenured males: (2/9)*250 = 55.55

Thus final ratio would be (16.667 + 4.44)/(66.66 + 55.55).

Please show me the fallacy in my logic.