Suppose that a certain disease is present in 10% of the population, and that there is a screening test designed to detect this disease if present. The test does not always work perfectly. Sometimes the test is negative when the disease is present, and sometimes it is positive when the disease is absent. The table below shows the proportion of times that the test produces various results.

a. Find the following probabilities from the table:
P(D), P(DC), P(N | DC), P(N | D).
b. Use Bayes' Rule and the results of part a to find P(D | N).
c. Use the definition of conditional probability to find P(D | N). (Your answer should be the same as the answer to part b.)
d. Find the probability of a false positive, that the test is positive, given that the person is disease-free.
e. Find the probability of a false negative, that the test is negative, given that the person has the disease.
f. Are either of the probabilities in parts d or e large enough that you would be concerned about the reliability of this screening method? Explain.

Transcribed Image Text:

Test Is Positive (P) .08 Test Is Negative (N) .22 Disease Present (D Disease Absent (D) .05 85