Question

"To diagnose colorectal cancer, the hemoccult test is conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who participate in
screening using the hemoccult test, the following information is available.
The probability that one of these people has colorectal cancer is 0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he will have a
positive hemoccult test. If a person does not have colorectal cancer, the
probability is 3 percent that he will still have a positive hemoccult test. Imagine a
person (over age 50, no symptoms) who has a positive hemoccult test in your
screening. What is the probability that this person actually has colorectal
cancer?"

using the above paragraphs

1. Calculate the probability that this person actually has colorectal cancer given a
positive test.
2. Based on your analysis, communicate your result to someone who thinks that
routine cancer screening tests for healthy persons are always a good idea.

Answer 1