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# 2 - Using clinical studies the following approximates to...

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2 Pr ( A B )= Pr ( B ) · Pr ( A | B ) Pr ( A | B )= Pr ( A B ) Pr ( B )
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nnnnnnnnnn 8 What is the probability that a family with two children has two boys, given they have at least one boy? Assume each of the possibilities BB, BG, GB, and GG are equally likely, where B represents a boy and G a girl. Note that the order does matter here.
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10 Diagnosing Tuberculosis . A convenient test for tuberculosis is purified protein derivative (PPD) skin test. This test is cheap but sometimes predicts a patient has tuberculosis when in fact he/she does not, and also it may show negative when in fact the patient has tuberculosis. T: event that patient has tuberculosis. P: event that patient’s test is positive.
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Unformatted text preview: Using clinical studies the following approximates to probabilities have been observed Estimate the probabilities that a patient who tested positive in fact has tuberculosis, and the probability that a patient who tested negative has tuberculosis. It is also known You may use Bayes’s Theorem: Let A and B be events. Then Pr ( B | A ) = Pr ( B ) · Pr ( A | B ) Pr ( A ) = Pr ( B ) · Pr ( A | B ) Pr ( B ) · Pr ( A | B ) + Pr ( B ) · Pr ( A | B ) Pr ( W | T ) = 0 . 775 , Pr ( W | T ) = 0 . 15 , Pr ( W | T ) = 0 . 225 , Pr ( W | T ) = 0 . 85 Pr ( T ) ≈ . 002 ....
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2 - Using clinical studies the following approximates to...

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