Explain Conditional probability.

Conditional probability uses Bayes theorem to calculate the relationships between the dependent events. If A and B are two events then P(AB) can be read as the probability of event occurring A given that the event B has already occurred. The equation of conditional probability can be written as

Let us take an example of an email classification system. The objective is to predict the spam messages based on the word lottery. In this case we already knew the prior probability of a spam message which is 10%. The marginal likelihood is the probability of the word lottery in all the messages which is 4%. Now, the probability that the lottery was used in previous spam messages and is called the likelihood.

By applying the Bayes theorem to the evidence, we can calculate the posterior probability that calculates the probability that the message is likely to be spam; given the fact that the lottery was appearing in message. On average if the probability is greater than 50 percent it indicates that the message is spam rather than ham.