Suppose that a bayesian spam filter is trained on a set of 500 spam messages and 200 mes- sages that are not spam. the word exciting appears in 40 spam messages and in 25 messages that are not spam.(1) would an incoming message be rejected as spam if it contains the word exciting and the threshold for rejecting spam is 0.9, on the assumption of flat priors (that is, 50% of incoming messages are spam)? calculate the probability and show all work.(2) what would be the probability that the message is spam if instead of flat priors we use information that, on average, 85% of messages received at this company are spam? (3) what would be the probability the message is spam if in addition to exciting it also contains the word rolex which appears in 30 of the spam messages and 20 innocent messages in the corpus, if, on average, 85% of messages received at this company are spam?