Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of 0.001). Of those who have the disease, 97% 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.

0.001
(b)
Use the general multiplication rule to calculate P(has disease and positive test).
(c)
Calculate P(positive test).
(d)
Calculate P(has disease | positive test). (Round your answer to five decimal places.)
Does the result surprise you? Give an intuitive explanation for why this probability is small.
This result is not surprising. This probability is small because so many more people have the disease than do not have the disease. The majority of people who have the disease and test positive greatly outnumber the people who do not have the disease and still test positive.
This result is surprising. This probability should not be small because so many more people do not have the disease than have the disease. The majority of people who have the disease and test positive greatly outnumber the people who do not have the disease and still test positive.
This result is not surprising. This probability is small because so many more people do not have the disease than have the disease. The majority of people who have the disease and test positive greatly outnumber the people who do not have the disease and still test positive.
This result is surprising. This probability should not be small because so many more people have the disease than do not have the disease. The majority of people who have the disease and test positive greatly outnumber the people who do not have the disease and still test positive.
This result is not surprising. This probability is small because so many more people do not have the disease than have the disease. The minority of people who do not have the disease but still test positive greatly outnumber the people who have the disease and test positive.