For the use of a test for a certain disease, the sensitivity is

0.9,

the specificity is

0.91,

and the prevalence is

0.006.

a. Given that a test is positive, find the probability that a random patient has the disease.

b. Draw a tree diagram for a typical sample of 1000 patients.

c. Of the cases that are positive, explain why the proportion in error is larger if the prevalence is lower.