Imagine that the proportion of all e-mails in our training data that are spam is .62, and the proportion of e-mails that are ham is .38. An e-mail comes through our Bayesian filter and it contains only two words: lucrative lottery. From our training data, we know the probabilities that each of these words would appear in either type of e-mail. The probabilities are shown below:

Using a naive bayes methodology, what is the probability that this e-mail is spam?

SPAM HAM lucrative .05 .01 lottery .15 .03 SPAM HAM lucrative .05 .01 lottery .15 .03