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A study reported by Forbes indicated that the five most common words appearing in spam
e-mails are shipping!, today!, here!, available, and fingertips! Many spam filters separate spam from ham (e-mail not considered to be spam) through application of Bayes' theorem. Suppose that for one e-mail account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam e-mail are given below.
shipping! .051
today ! .045
here! .034
available .014
fingertips ! .014
Also suppose that the proportions of ham messages that have these words are
shipping! .0015
today ! .0022
here! .0022
available .041
fingertips ! .041
- 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? - If a message includes the word today!, what is the probability the message is spam? 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?
- 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?
- What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?
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Bundle: Essentials of Modern Business Statistics with Microsoft Office Excel, Loose-leaf Version, 7th + LMS Integrated for MindTap Business Statistics, 1 term (6 months) Printed Access Card
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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