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CHAPTER 3   CONDITIONAL PROBABILITY

       This chapter extends the concept of probability to conditional probability, notes a special case of interest (independence) and then uses definitions/results from previous chapters to state and prove the two great Theorems of Probability theory.

• The Theorem of Total Probability

                A theorem that is the consequence of the Probability Axioms, the concept of a partition, and the
                conditional probability definition. It provides a general method of calculation for probabilities of
                complex events.

• Bayes Theorem

                A theorem that is the consequence of the conditional probability definition, it allow reverse or inverse
                probability calculations. 

The canonical example for both of these theorems is the medical screening example; a population comprises sufferers and non-sufferers from a particular disease, who are individually tested using a good but fallible test.  Inference about the disease status is required on the basis of the test result, which is either positive (indicating a sufferer) or negative (indicating a non-sufferer).    Probability calculations reveal that the rates of false positives (positive test for a non-sufferer),  false negatives (negative test for a sufferer), and the overall population proportion of sufferers all play a crucial role in determining the worth of the test.