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 2:
We want to find the probability described in bold font above.
Write this probability using symbols, such as the ones we defined in the first hint.
In symbols, we want to find P(A1/B).