# Intuitive logic behind Naive Bayes and Bayes Theorem. Why does Naive Bayes multiply/input prior probability twice?

In order to calculate Naive Bayes, we combine prior probability with test evidence and obtain posterior probability.

When calculating test instance, we combine the probability of the test with the prior probability i.e. test given prior condition. The resulting test evidence (test given prior condition) is multiplied AGAIN to prior probability before we move on to find posterior probability as a fraction of all probability in this universe.

What is the conceptual logic behind multiplying/inputting the prior probability twice? Looking at this question on the other end, what is the difference between x given y and y given x. (E.g. Cancer given positive test results, and positive results given cancer.) In my naive intuition, you'd still have cancer AND a positive test result in both cases.

• What do you mean by twice? Maybe you could refer to Bayes theorem formula and point the part you mean? Alternatively, maybe you could give us worked example with pointing the confusing part? – Tim Dec 20 '18 at 15:28