Problem 4. Suppose that a Bayesian spam filter is trained on a set of 1000 spam messages and 250 messages that are not spam. The word "cruise" appears in 50 spam messages and in 2 messages that are not spam, while the word "urgent" appears in 100 spam messages and in 10 messages that are not spam. Would an incoming message be rejected as spam f t contains both words "cruise" and "urgent" and the threshold for rejecting spam is 0.9? (Assume, for simplicity, that the message is equally likely to be spam as it is not to be spam and that the two words are used independently.) Provide detailed justifications for your answers