Question

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, 1 in every 10 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! 0.049 0.044 0.034 0.013 0.013 Also suppose that the proportions of ham messages that have these words are shipping! 0.0015 today! 0.0023 here! 0.0023 available 0.0041 fingertips! 0.0010 Rour your answers to three decimal places. a. a message des the worshipping ng is the probab message is spam? a mes geinc des worshi ingl, wristbyrobability me ge is ham ould messa that include the word shipping! be flagged as spam? - Select your answer - A b. 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? mit Select your answer - y? use the probility - Select answer - If a my sa include the word vall ple, who is the bability ne mes geism ? If a medge include thord fings!, what is the rooility the meeis ?

Answer 1

E by Toda P ( the message is spam | the message includes today) PC * Today 1 Apam".). P.C.". spomi") P ("Today Ispam") .P (spam) + P(* Today'! *Htam") = f("Ha") 0:044 x 50 - - -68 (Am) 044x1,0 +0023 x % P. (. The mag. is spain | The may includes "here ") PC Here" i "Spam") · P (Spam") ple Here." Spomin). PC Spom ") + PC Here " i polizia ) -PC" framt). 1034.% . *4034 * + : 0023 x 9 para 1 3.6216 ( Aug