Before diving into Naive Bayes, it would be good to reiterate the fundamentals. Probability of an event can be estimated from observed data by dividing the number of trails in which an event occurred with the total number of trails. For instance, if a bag contains red and blue balls and randomly picked 10 balls one by one with replacement and out of 10, 3 red balls appeared in trails we can say that probability of red is 0.3, pred = 3/10 = 0.3. Total probability of all possible outcomes must be 100 percent.
If a trail has two outcomes such as email classification either it is spam or ham and both cannot occur simultaneously, these events are considered as mutually exclusive with each other. In addition, if those outcomes cover all possible events, it would be called as exhaustive events. For example, in email classification if P (spam) = 0.1, we will be able to calculate P (ham) = 1- 0.1 = 0.9, these two events are mutually exclusive. In the following Venn diagram, all the email possible classes are represented (the entire universe) with the type of outcomes:
