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At a track meet 2/5 of the first place finishers went to Ohio State. One half...

At a track meet 2/5 of the first place finishers went to Ohio State. One half of Ohio State's first place finishers were women. If 2/9 of the first place finishers who did NOT attend Ohio State were women, what fractional part of the total number of first place finishers were men?

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Answer #1

P(female) =P(went to Ohio)*P(female|went to Ohio)+P(not went to Ohio)*P(female|not went to Ohio)

=(2/5)*(1/2)+(1-2/5)*(2/9) =1/3

therefore P(male) =1-P(female) =1-1/3 =2/3

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