iven A. A second derivation of Bayes Theorem gives the rule for updating belief in a Hypothesis A (i.e. the probability of A) given additional evidence B. This is shown in equation 2 Where A* is the false outcome of an argument. The left hand term, P(A|B) is called the posterior probability, and it gives the probability of the hypothesis A after considering the evidence B. P(A|B) is called the likelihood, and it gives the probability of evidence assuming the hypothesis B and the background information is true.In many situations, predictions of outcomes involve probabilities, one theory might predict that a certain outcome has a twenty percent chance of happening; another may predict a sixty percent chance of the same outcome. In these types of situations, the actual outcome would tend to shift our degree of belief from one theory to the other. As previously noted, Bayes theorem gives a way to calculate this experience or "degree of belief" (Logue 1995, pg.95). To construct an example of Bayes' theorem, one begins by designing a mutually exclusive and all-inclusive hypothesis. That is, an hypothesis that includes all out comes. Next, one needs to spread out the degree of belief among them by assigning a probability based on what we believe to be true, to each hypothesis. This assignment would be between zero and one to make it all-inclusive. Not the often misused probability such as a person saying, "I am behind you one hundred and ten percent", for such a statement to be true is not only physically impossible but certainly falls outside the requirement of being all inclusive. If one has no prior basis in either experience, or observation of the hypothesis, one simply spreads out he probabilities evenly among the hypothesis.The next step in setting up the equation is to construct a list of possible outcomes. The list of possible outcomes, like the hypothesis, should also be mutually exclusive and all-inclusive. Each hypoth...
