I'm not sure how to answer this question, and the assignment is due very soon. I don't need detailed explanations, just the basic working out.

1. [10 pts] A spam filter usually identifies spam emails by looking at the words contained in an email. Suppose that (i) 40% emails are spam; (ii) 1% of spam emails contain the word "lottery"; and (iii) 0.01% of non-spam emails contain the word "lottery". Suppose that an email is received that contains the word "lottery". What is the probability that the email is spam