Medical Test A scientist designed a medical test for a certain disease. Among 100

Chapter 8, Problem 50

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Medical Test A scientist designed a medical test for a certain disease. Among 100 patients who have the disease, the test will show the presence of the disease in 97 cases out of 100, and will fail to show the presence of the disease in the remaining 3 cases out of 100. Among those who do not have the disease, the test will erroneously show the presence of the disease in 4 cases out of 100, and will show that there is no disease in the remaining 96 cases out of 100. (a) What is the probability that a patient who tested positive on this test actually has the disease, if it is estimated that 20% of the population has the disease? (b) What is the probability that a patient who tested positive on this test actually has the disease, if it is estimated that 4% of the population has the disease? (c) What is the probability that a patient who took the test twice and tested positive both times actually has the disease, if it is estimated that 4% of the population has the disease?