The probability that an individual randomly selected from a particular population has a certain disease is .05. A diagnostic test correctly detects the presence of the disease 98% of the time and correctly detects the absence of the disease 99% 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.]
The probability that an individual randomly selected from a particular population has a certain disease is .05. A diagnostic test correctly detects the presence of the disease 98% of the time and correctly detects the absence of the disease 99% 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.]
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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![The probability that an individual randomly selected
from a particular population has a certain disease is .05.
A diagnostic test correctly detects the presence of the
disease 98% of the time and correctly detects the absence
of the disease 99% 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-geneeration branches corresponding to Disease
and No Disease, and second- and third-generation
branches corresponding to results of the two tests.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21a1aa0c-d135-48cc-aaef-e1f1c96ff403%2F2267b13d-ba1d-4543-a41b-d7d726cefe5c%2F1wg5nkcn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The probability that an individual randomly selected
from a particular population has a certain disease is .05.
A diagnostic test correctly detects the presence of the
disease 98% of the time and correctly detects the absence
of the disease 99% 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-geneeration branches corresponding to Disease
and No Disease, and second- and third-generation
branches corresponding to results of the two tests.]
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