Question

The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 as a routine part of a physical exam, with levels above 4 ng/mL indicating possible prostate cancer. The test result is not always correct, sometimes indicating prostate cancer when it is not present and often missing prostate cancer that is present. Suppose that these are the approximate conditional probabilities of a positive (above 4 ng/ml) and negative test result given cancer is present or absent. In a large study of prostate cancer screening, it was found that about 6.2% of the population has prostate cancer. Draw a tree diagram for selecting a person from this population (outcomes: cancer present or absent) and testing his blood (outcomes: test positive or negative).

Answer 1

The missing table for the Test Result can be expressed as:

Test Result

Positive Negative

Cancer Present 0.21 0.79

Cancer Absent 0.06 0.94

Answer:

Explanation:

A tree diagram is an elegant way of determining an exhaustive list of sample elements in the sample space. It is by finding the ordered n-tuples of the elements in the events under consideration.

The tree diagram for selecting a person from the population in the given question can be found in the attached image below.