The five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email account, in every messages is spam and the proportions of spam messages that have the five most common words in spam email are given below. shipping! today! here! available fingertips! Also suppose that the proportions of ham messages that have these words are shipping! today! here! available fingertips! Round your answers to three decimal places. 1. If a message includes the word shipping!, what is the probability the message is spam? Should messages that include the word shipping! be flagged as spam?
2. If a message includes the word today!, what is the probability the message is spam?
3. If a message includes the word here!, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? Because the probability is
4. If a message includes the word available, what is the probability the message is spam? If a message includes the word fingertips!, what is the probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? Because the probability is
5. What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively? Explain. It is easier to distinguish spam from ham when a word occurs MORE? OR LESS? in spam and less often in ham.