Q# The probability that an individual randomly selected from a particular popula

Question

Q# 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 93% of the time and correctly detects the absence of the disease 92% 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.]

Refrence: Probability and Statistics for Engineering and the Sciences -9th Ed. Author: Devore, Jay L.

Thank you

Explanation / Answer

c - correct detection of disease

d - disease

nd - absence of disease.

P(c/d) p( c AND d)/ p(d)                         0.9300 p( c AND d) P(c/d) * p(d)                         0.0558 p(c/nd) p( c AND nd)/ p(d)                         0.9200 p( c AND nd) P(c/nd) * p(d)                         0.0552 p(d) 0.06 p ( c) p( c AND d)+ p (c AND nd)                              0.11 p (d/c) p(d AND c)/ p ( c)                              0.50

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