Reference no: EM13179190
A diagnostic test is a procedure which gives a quick, but not always reliable, indication of whether a patient has a certain disease. Test results are said to be "positive" if, after testing, the person is thought to have the disease and "negative" if the person is thought not to have the disease.
In a particular region, 4% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 95% of the people who have the disease. However, the test also incorrectly diagnoses 9% of those who do not have the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do).
A randomly selected person in the region is tested for the disease.
(a) What is the probability the test comes back positive?
(b) What is the probability the test comes back positive and the person actually has the disease?
(c) If the test comes back positive, what then is the conditional probability that the person actually does have the disease?
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What is the probability the test comes back positive
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