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In a Random Sample of UTC Students 50% Indicated They

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In a random sample of UTC students 50% indicated they are business majors, 40% engineering majors, and 10% other majors. Of the business majors, 60% were females; whereas, 30% of engineering majors were females. Finally, 20% of the other majors were female.
a.What percentage of students in this sample was female?
b.Given that a person is female, what is the probability that she is an engineering major?


Definitions:

Dichotomy

A division or contrast between two things that are represented as being entirely different.

Analogy

A comparison between two things, typically for the purpose of explanation or clarification, highlighting similarities in some respects.

False Dichotomy

A logical fallacy that presents two opposing options as the only possibilities, when in fact more options exist.

Weak Analogy

An argument based on insufficient parallels between two or more entities, which may lead to faulty conclusions.

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