lect10v1 - Stat 104 Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 10: Introduction to Probability, Part III 1
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Bayes’ Theorem s One important point about conditional probability is that (usually) P(A|B) does not equal P(B|A). s Some books make a big deal out of this but its not that fancy a concept. s The usual example concerns drug testing; it’s a good example to study since it focuses us on why its important to understand what one is conditioning on. 2
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Urine or You’re Out s Suppose the Incredibly Rapid Rooter Plumbing Company wants to drug test their employees. s They purchase a test with the following characteristic : 3 P(test + | actual drug user) = 98%.
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What do we want to condition on? s You always condition on what you know , so for an employer’s legal department, they need to know P(actual drug user | test +). s That is, what is the chance the test will be correct ? s Just because P(A|B) is near 100% doesn’t imply P(B|A) has to be near 100%. s That is, P(test+|Druggie)=.98 doesn’t mean P(Druggie|test+) = 0.98 4
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s Suppose also that P(test - | non drug user) = 90% and that Rapid Rooter also has good reason to suspect that 10% of his employees are drug users. s Using the multiplication rule we can create the usual 2x2 table. 5
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lect10v1 - Stat 104 Quantitative Methods for Economists...

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