6. Assume that cancer has a 1% prevalence rate, meaning that 1% of the population has cancer. Denoting the event of having cancer by C, we have P(C) =0.01 for a subject randomly selected from the...

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Extracted text: 6. Assume that cancer has a 1% prevalence rate, meaning that 1% of the population has cancer. Denoting the event of having cancer by C, we have P(C) =0.01 for a subject randomly selected from the population. This result is included with the following performance characteristics of the test for cancer (based on Probabilistic Reasoning in Clinical Medicine by David Eddy, Cambridge University Press). Find P(C|positive test result). That is, find the probability that a subject actually has cancer given that he or she has a positive test result. • P(C)= 0.01 (There is 1% prevalence rate of the cancer) The false positive rate is 10%. That is, P(positive test result given that cancer is not present) 0.1 %3D The true positive rate is 80%. That is , P(positive test result given that cancer is present) = 0.1 %3D Positive Test Result Negative Test Result (Test shows no cancer) Total (Test shows cancer) Cancer 8. 10 (True Positive) (False negative) No Cancer 99 891 990 (False Positive) (True Negative)