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Elementary probability theory

Diagnosis tests of medical conditions have several results. The test result can be positive or negative, whether or not a patient has the condition. A positive test(+) indicates the patient has the condition. A negative (-) test indicates that a patient does not have the condition. Remember, a positive test does not prove that the patient has the condition. Additional medical test may be required.Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Conditions Conditions Row Total
presents Absent

Test results + 110 20 130

Test Results - 20 50 70

Column Total 130 70 200

Assume the sample is representing of the entire population. For a person selected at random, compute the following probabilities.

a) P(+, given condition present);this is known as the sensitivity of a test.
b) P( -, given condition present); this is known as the false-negative rate.
c) P( -, given condition absent); this is known as the specificity of a test.
d) P( +, given condition absent); this is known as the false - positive rate.
e) P( condition presents and +);this a predictive of the test.
f) P( condition presents and - )

Solution Preview

Conditions Conditions Row Total
presents Absent

Test results + 110 20 130

Test Results - 20 50 70

Column Total 130 70 200

Assume the sample is representing of ...

$2.19