Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of .001). Of those who have the disease, 95% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the test.
a. Construct a tree diagram having two first-generation branches, for has disease and doesn't have disease, and two second-generation branches leading out from each of these, for positive test and negative test. Then enter appropriate probabilities on the four branches.
b. Use the general multiplication rule to calculate P(has disease and positive test).
c. Calculate P(positive test).
d. Calculate P(has disease upositive test). Does the result surprise you? Give an intuitive explanation for why this probability is small.