Understanding Bayes theorem with conditional probability

Conditional probability provides a way of calculating relationships between dependent events using Bayes theorem. For example, A and B are two events and we would like to calculate P(A\B) can be read as the probability of event occurring A given the fact that event B already occurred, in fact this is known as conditional probability, the equation can be written as follows:

To understand better, we will now talk about the email classification example. Our objective is to predict whether email is spam given the word lottery and some other clues. In this case we already knew the overall probability of spam, which is 10 percent also known as prior probability. Now suppose you have obtained an additional piece of information that probability of word lottery in all messages, which is 4 percent, also known as marginal likelihood. Now, we know the probability that lottery was used in previous spam messages and is called the likelihood.

By applying...