# Question

In the lesson on spam filtering using Bayes’ theorem, we’re asked to determine whether or not an email should be classified as spam given that it contains the word *enhancement*. In real world scenarios we can’t make a good decision based only on one word. How can we expand this approach to multiple words?

# Answer

Recall that in writing `P(A|B)`

, `A`

and `B`

are just **events**. So, simply, they can be more complex than just a single word. If we want to make this Bayes spam filter more realistic, we can look at each of the words `w1, w2, ... ,wn`

in the email and consider

`P(spam | w1, w2, ... , wn)`

the probability that the email is spam given *all* the words in the email under consideration. It may look a bit more involved but the ways that we compute the probabilities are not much more complicated; `B`

just happens to equal `w1, w2, ..., wn`

:

`P(w1, w2, ... , wn)`

is the probability that each of these words appear in any email

`P(w1, w2, ... , wn | spam)`

is the probability that a spam email contains each of these words