Complete the two functions in the two cells below.

The first trains$/$learns a naive Bayes classifier. The second predicts the classes for a set of examples based on the model learned.

Hint: You'll need to generate the data matrix yourself and your own testing examples.

Hint $2$: You will have to deal with counts that are $0.$ Leaving them as zero will result in $0$ probabilities that will cause problems. A standard way to handle this is to add $1$ to all counts. For frequent feature values, it does not change things much. For infrequent values, it keeps them away from $0$ and admits that they might happen more often