The specificity of a diagnostic test for a disease is the probability that the test will be negative when administered to a person who does not have the disease. The higher the specificity, the lower the false positive rate. Suppose the specificity of a diagnostic procedure to test whether a person has a particular disease is 89%. a. A person who does not have the disease is tested for it using this procedure. What is the probability that the test result will be positive? b. A person who does not have the disease is tested for it by two independent laboratories using this procedure. What is the probability that both test results will be positive?
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The probability that the test result will be positive is 89%. Show more…
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A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.93. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.03. It is estimated that 3% of the population who take this test have the disease. (Round your answers to three decimal places.) (a) If the test administered to an individual is positive, what is the probability that the person actually has the disease? (b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)
Sri K.
A diagnostic test has a 95% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who doesn't have the disease. It is estimated that 15% of the population suffers from this disease. (a) What is the probability that a test result is positive? (b) A person receives a positive test result. What is the probability that this person actually has the disease? (probability of a true positive) (c) A person receives a positive test result. What is the probability that this person doesn't actually have the disease? (probability of a false negative)
Ahmad R.
a) A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a "false positive" result for 1% of the healthy persons tested. (That is, if a healthy person is tested, then, with a probability of 0.01, the test result will imply he or she has the disease.) If 0.5% of the population actually has the disease, what is the probability a person has the disease given that the test result is positive? b) What is the probability that a randomly selected person, who has the disease, gets a positive result from the blood test? Explain the difference between this probability and the probability you calculated in a). c) Are the two events that a person has the disease and that the blood test is positive dependent? Does the fact that a test result was positive increase the risk of having the disease, compared to the probability that a random individual from the population has the disease?
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