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The probability that an individual randomly selected from a particular population has a certain disease is...

The probability that an individual randomly selected from a particular population has a certain disease is 0.06. A diagnostic test correctly detects the presence of the disease 92% of the time and correctly detects the absence of the disease 93% of the time. If the test is applied twice, the two test results are independent, and both are positive, what is the (posterior) probability that the selected individual has the disease? [Hint: Tree diagram with first-generation branches corresponding to Disease and No Disease, and second- and third-generation branches corresponding to results of the two tests.]

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