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# quiz2.new.sol - does not have tuberculosis Solution Applied...

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Raquel Prado Applied Mathematics and Statistics AMS-7. Winter 2008 Name: Quiz 2 Among the 1820 subjects in a study, 30 sufered From tuberculosis and 1790 did not. Chest x-rays were administered to all individuals; 73 had a positive x-ray—implying that there was signi±cant evidence oF in²ammatory disease—whereas the results oF the other 1747 were negative. The data For this study are presented in the table below. Tuberculosis x-ray No Yes Total Negative x-ray 1739 8 1747 Positive x-ray 51 22 73 Total 1790 30 1820 1. (20 points) What is the probability oF a positive x-ray given that a subject has tuberculosis? Solution. P ( T + | D ) = 22 30 = 0 . 733 2. (10 points) What is the probability oF a negative x-ray given that a subject has tuberculosis? Solution. P ( T - | D ) = 1 - 22 30 = 8 30 = 0 . 267 3. (20 points) What is the probability oF a positive x-ray given that a subject

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Unformatted text preview: does not have tuberculosis? Solution. Applied Math and Statistics Quiz 2 AMS-7. 2 P ( T + | ¯ D ) = 51 1790 = 0 . 0285 4. (10 points) What is the probability of a negative x-ray given that a subject does not have tuberculosis? Solution. P ( T-| ¯ D ) = 1739 1790 = 0 . 9715 5. (40 points) Assume that the probability that an individual in the general pop-ulation has tuberculosis is 0.000093. What is the probability that a randomly selected individual has tuberculosis given that his or her x-ray is positive? (Hint: use Bayes’ rule). Solution. P ( D | T + ) = P ( T + | D ) P ( D ) P ( T + | D ) P ( D ) + P ( T + | ¯ D ) P ( ¯ D ) = . 733 × . 000093 . 733 × . 000093 + 0 . 0285 × . 999907 = 0 . 00239...
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quiz2.new.sol - does not have tuberculosis Solution Applied...

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