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. Test Result
Positive Negative
Cancer present 0.21 0.79
Cancer absent 0.06 0.94
In a large study of prostate cancer screening, it was found that about 6.5% of the population has prostate cancer.
A. 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).
B. What is the probability that the test is positive for a randomly chosen person from this population?