Test for a Disease. We have just received word that we have tested positive for a disease. The test was 90 percent reliable. We want to know the probability that we have the disease after we learn that the result of the test is positive. Some readers may feel that this probability should be about 0.9. however, this feeling completely ignores the small probability of 0.0001 that you had the disease before taking the test. We shall let B1 denote the event that you have the disease, and let B2 denote the event that you do not have the disease, The event B1 and B2 form a partition. Also, let A denote the event that the response to the test is positive. The event A is information we will learn that tells us something about the partition elements. Then, by Bayes’ theorem, P(B1∣A)=