Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (-) indicates that the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work 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 a condition are shown. Condition Absent Row Total 130 70 200 Condition Present Test Result + 110 20 Test Result - 19 51 Column Total 129 71 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.) (a) P(+ | condition present); this is known as the sensitivity of a test. (b) P(- | condition present); this is known as the false-negative rate. (c) P(- | condition absent); this is known as the specificity of a test. (d) P(+ | condition absent); this is known as the false-positive rate. (e) P(condition present and +); this is the predictive value of the test. (f) P(condition present and-).
Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (-) indicates that the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work 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 a condition are shown. Condition Absent Row Total 130 70 200 Condition Present Test Result + 110 20 Test Result - 19 51 Column Total 129 71 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.) (a) P(+ | condition present); this is known as the sensitivity of a test. (b) P(- | condition present); this is known as the false-negative rate. (c) P(- | condition absent); this is known as the specificity of a test. (d) P(+ | condition absent); this is known as the false-positive rate. (e) P(condition present and +); this is the predictive value of the test. (f) P(condition present and-).
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 4SE: What is the difference between events and outcomes? Give an example of both using the sample space...
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Transcribed Image Text:Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A
positive test (+) indicates that the patient has the condition. A negative test (-) indicates that the patient does not have the condition. Remember, a positive
test does not prove the patient has the condition. Additional medical work 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 a condition are shown.
Condition Present
Condition Absent
Row Total
20
130
Test Result +
Test Result -
Column Total
110
19
51
70
129
71
200
Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as
fractions.)
(a)
P(+ | condition present); this is known as the sensitivity of a test.
(b)
P(- | condition present); this is known as the false-negative rate.
(c)
P(- | condition absent); this is known as the specificity of a test.
(d)
P(+ | condition absent); this is known as the false-positive rate.
(e)
P(condition present and +); this is the predictive value of the test.
(f)
P(condition present and -).
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