The incidence of prostate cancer among men in the US over 65 years of age is...

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The incidence of prostate cancer among men in the US over 65 years of age is 60% (!). A blood test for elevated levels of prostate-specific antigen (PSA) is used as one indicator of prostate cancer. The accuracy of this test is tabulated below where the entries are the conditional probabilities P [test result | state] for the two states S1- have prostate cancer and S2 – do not have prostate cancer. P [test result | state] State S1 – have prostate cancer State S2 – do not have prostate cancer Test: positive 0.95 0.78 Test: negative 0.05 0.22 A PSA test has been run on a man over 60 and the result is negative. What is the revised probability that he in fact does NOT have prostate cancer? Be sure to show your work. The incidence of prostate cancer among men in the US over 65 years of age is 60% (!). A blood test for elevated levels of prostate-specific antigen (PSA) is used as one indicator of prostate cancer. The accuracy of this test is tabulated below where the entries are the conditional probabilities P [test result | state] for the two states S1- have prostate cancer and S2 – do not have prostate cancer. P [test result | state] State S1 – have prostate cancer State S2 – do not have prostate cancer Test: positive 0.95 0.78 Test: negative 0.05 0.22 A PSA test has been run on a man over 60 and the result is negative. What is the revised probability that he in fact does NOT have prostate cancer? Be sure to show your work.

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