Question

Suppose there is a test for prostate cancer for men over 50 that is 95% accurate both for men that do and for men that dont have prostate cancer. (So the false positive and the false negative rates are both 59). If 1.2 percent of males over 50 have prostate cancer, compute the probability that a Steve, a man over 50, has prostate cancer, given that his test result was positive.

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Answer:

From the given information we can form the table for a 1000 persons with above 50 years age.

Cancer

No cancer

Total

test +ve

114

44

158

test -ve

6

836

842

Total

120

880

1000

The required probability P( cancer/test+ve) = 114/158

=0.721519

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