The Problem: Analysis of Cancer Screening Procedure Accuracy
A patient undergoes an experimental procedure meant to allow early identification of a particular type of cancer. Her results indicate that she does, in fact, have cancer. However, since it is a novel procedure, the test's accuracy is not yet trusted. Before revealing the results to the patient then, her oncologist must find the probability that the patient has cancer given that the test says she has cancer. The only data collected about this procedure is as follows:
The prevalence of the type of cancer identified by the test is 0.0001.
The probability of a positive test result given the patient actually has cancer is 0.9.
The probability of a false positive test result is 0.001.
The prevalence of the type of cancer identified by the test is 0.0001.
The probability of a positive test result given the patient actually has cancer is 0.9.
The probability of a false positive test result is 0.001.
Hint 4:
An event A and its complement Ac partition a set, so the sum of the probabilities of an event and its complement is 1:
P(A) + P(Ac) = 1
Recall from Hint 1 that the events of having cancer, (A1), and not having cancer, (A2), partition the set of living individuals at any given time.
The complement of having cancer is not having cancer, so P(A2) = 1 - P(A1).
An event A and its complement Ac partition a set, so the sum of the probabilities of an event and its complement is 1:
P(A) + P(Ac) = 1
Recall from Hint 1 that the events of having cancer, (A1), and not having cancer, (A2), partition the set of living individuals at any given time.
The complement of having cancer is not having cancer, so P(A2) = 1 - P(A1).