The five most common words appearing in spam emails are shipping!, today!, here!,available, and fingertips! (Andy Greenberg, “The Most Common Words In Spam Email,”Forbes website, March 17, 2010). Many spam filters separate spam from ham (email notconsidered to be spam) through application of bayes’ theorem. Suppose that for one emailaccount, 1 in every 10 messages is spam and the proportions of spam messages that havethe five most common words in spam email are given below.shipping! .051today! .045here! .034available .014fingertips! .014Also suppose that the proportions of ham messages that have these words areshipping! .0015today! .0022here! .0022available .0041fingertips! .0011a. If a message includes the word shipping!, what is the probability the message is spam?If a message includes the word shipping!, what is the probability the message is ham?Should messages that include the word shipping! be flagged as spam?b. If a message includes the word today!, what is the probability the message is spam? Ifa message includes the word here!, what is the probability the message is spam? Whichof these two words is a stronger indicator that a message is spam? Why?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.