The prostate-specific antigen (PSA) test is a simple blood test to screen for pr
ID: 3304145 • Letter: T
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.
What is the probability that the test is positive for a randomly chosen person from this population? (Enter your answer to five decimal places.)
P(Positive test) =
Explanation / Answer
Here we are given that P( cancer ) = 0.066 as 6.6% of the population has prostrate cancer.
Using Bayes theorem, Probability that the test is positive for a randomly chosen person from this population is computed as:
P( positive ) = P( positive | cancer present ) P( cancer present ) + P( positive | cancer absent ) P( cancer absent )
P( positive ) = 0.21*0.066 + 0.06*(1 - 0.066) = 0.01386 + 0.05604 = 0.0699
Therefore 0.0699 is the required probability here that the test is positive for a randomly chosen person from this population.
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