A test for a certain disease is found to be 95% accurate, meaning that it will...

A test for a certain disease is found to be 95% accurate, meaning that it will correctly diagnose the disease in 95 out of 100 people who have the ailment. The test is also 95% accurate for a negative result, meaning that it will correctly exclude the disease in 95 out of 100 people who do not have the ailment. For a certain segment of the population, the incidence of the disease is 4%. (1) If a person tests positive, find the probability that the person actually has the disease (Hint: define appropriate events and use Bayes Theorem); (2) Now suppose the incidence of the disease is 49%. Compute the probability that the person actually has the disease, given that the test is positive; (3)The probability you obtained in (1) is much smaller than 0.95, if your computation is correct. Hence, You can conclude that there is only a much smaller probability to claim “the person really has the disease” after knowing that “the test is positive”, though the test has 95% “correctness”. Explain this difference.

Hint.Population: the segment of the populationExperiment: Determine whether or not a selected person has the diseaseOutcomes: D, Dc (where D and Dc are defined below)Sample space: S = {D, Dc}Define necessary events: D = the selected person has the disease; Dc = the selected person does not have the disease. Rate of disease = 4%  P(D) = 4% , P(Dc) = 96% E = Testing result shows positive for the selected person Ec = Testing result shows negative for the selected person Correctness of testing: if the selected person does have the disease, the testing will show positive with probability 95%, i.e., (about) 95 positive out of 100 persons who do have the disease.if the selected person does NOT have the disease, the testing will show negative with probability 95%, i.e., (about) 95 positive out of 100 persons who do NOT have the disease.In other words, P(E | D) = 95% and P(Ec | Dc) = 95% Want P(D | E) = ?

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orchestra answered 2 years ago

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