Screening tests are often used in clinical practice to assess the likelihood that a person has a medical condition. The rationale is that, if disease is identified before symptom onset, then earlier treatment may lead to cure or improved survival or quality of life. The prostate-specific antigen (PSA) test for prostate cancer measures blood concentrations of PSA, a protein produced by the prostate gland. Elevated levels of PSA may help identify men with prostate cancer. A definitive diagnosis, however, requires biopsies of the prostate gland. A population of 500 men over 50 years old who are considered at high risk for prostate cancer had both the PSA screening test and a biopsy. Among these men, 12% had both elevated PSA levels and a positive biopsy, whereas 16% had low PSA levels and a negative biopsy. 18% had a positive biopsy. Hint: Start by drawing a contingency table or Venn diagram.

What is the probability a randomly chosen man has an elevated PSA level? (3 points)

What is the probability that a randomly chosen man has a positive biopsy given that he has a low PSA level? (3 points) 

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