, you take the number that really does (100) and divide it by the number that would have tested positive but do not have it (2,475) and you get the probability that you really do have the cancer. 100/2,475 = 0.039. In other words, there is a 3.9% chance that you have the cancer (see equation 4).This calculation shows why it is important to take account of the overall incidence of the cancer in the population. This, in the Bayesian way of thinking, is known as prior probability. Being able to calculate results based on this prior probability, either known, speculated or not known, is the advantage of using Bayes' theorem. In our case, in a population of 10,000 with a cancer having an incidence rate of 1%, a test reliability of 75% will produce 2,475 false positives. Thus far outweighs the number of actual cases, which are only 100. As a result, if your test comes back positive, the chances are overwhelming that you are in the false positive group. This data, as it is placed in Bayes' theorem flows like this: Let P(H) represent the probability that the hypothesis is correct in the absence of any evidence - the prior probability. Therefore, H is the hypotheses that you have the cancer and P(H) is 0.01. You then take the test and get a positive result, this evidence of cancer we will call C. Let P(H|C) be the probability that H is correct given the evidence C. This is the revised estimate we want Bayes' theorem to calculate. Let P(C|H) be the probability that C would be found if H did occur. In our example, the test always detects cancer when it is present so P(C|H) = 1. To find the new estimate, you have to calculate P(H-wrong), the probability that H does not occur, which is .099 in this case. Finally, you have to calculate P(C|H-wrong), the probability that the Cancer C would be found (i.e., a positive test) even though H did not actually occur (i.e., you do not have the cancer), which is 0.25 in the example. In equatio...
