he five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters eparate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email ccount, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam mail are given below. chipping! oday! mere! available ingertips! 0.049 0.044 0.035 0.012 0.012 Iso suppose that the proportions of ham messages that have these words are chipping! 0.0013 oday! 0.0023 ere! 0.0023 vailable 0.0039 ingertips! 0.0010 ound your answers to three decimal places.

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