Now the question is, how do we use this wonderful Bayes theorem to do machine learning. And the answer is repeatedly. Let’s look at this example, a spam email classifier. So let’s say, we have some data in the form of a bunch of emails. Some of them are spam and some of them are not spam, which we call ham. Spam are, “Win money now!” “Make cash easy!” et cetera. And the ham are, “How are you?” “There you are!” et cetera. And now, what we’ll do is, a new email comes in say, “easy money” and we want to check if it’s spam or ham. So, we take it word by word. Of course, we can be more effective if we took into account the order of the words, but for this classifier, we won’t. It’s surprising how good it can be even if it doesn’t take into account the order of the words. So let’s study the first word say, “easy.” We can see that the word “easy” appears once among the three spam emails and once among the five ham emails. And the word “money” appears twice among the three spam emails and once among the five ham emails. So, let’s start with calculating some preliminary probabilities as an exercise. Given the data we have, what is the probability of an email containing the word “easy” given that it is spam? Here are some options. And let’s also calculate it for the other word. Again given our data, what’s the probability of an email being spam given that it contains the word “money”? Here are the options. Enter your answer below.