Problem $2$: $($Classification using probabilities$)$

One way to design a spam filter is to look at the words in an email. In partic$-$

ular, some words are more frequent in spam emails. Suppose that we have the

following information:

$40\%$ of emails are spam.

$9\%$ of spam emails contain the word "refinance".

$0\mathrm{.}01\%$ of non$-$spam emails contain the word "refinance".

Suppose that an email is checked and found to contain the word "refinance".

What is the probability that the email is spam?