There is a rare disease that only happens to 1 out of 100,000 people. A test shows
Question:
There is a rare disease that only happens to 1 out of 100,000 people. A test shows positive 99% of times when applied to an ill patient and, 1% of times when applied to a healthy patient. Please answer the following questions.
1. What is the probability for you to have the disease given that your test result is positive?
2. What is the probability for you to have the disease when you did two tests and both of them show positive? Assume that two tests are conducted independently.
3. Assume that the patient keeps on trying the test, what is the minimum number of tests that the patient has to try to be 99% percent sure that he is actually ill? Assume that all tests are conducted independently.
Statistics The Art and Science of Learning from Data
ISBN: 978-0321755940
3rd edition
Authors: Alan Agresti, Christine A. Franklin