Hi how is the naive bayes product derived from Bayes theorem? thanks!
If I understand your question correctly, Naive Bayes “product” is not derived form Bayes Rule. It is just the assumption (incorrect one but useful in our case) that variables (in our case - words) are independent of each other. Because of this assumption we can multiply words’ probabilities to get the probability of a sentence. (You can multiply probabilities of the independent events to get the probability of the whole sequence).
This assumption is incorrect because words do depend on each other. But it is useful in some applications because maybe the accuracy of this kind of model is acceptable, or it is just a baseline for a more sophisticated model.