Bayeaian 8pam Filtora uppce his e ece ed b e als and categonze each c ther as te

Question

Bayeaian 8pam Filtora uppce his e ece ed b e als and categonze each c ther as ter 5pam or ham ar y emi l that axampia,you fird a.0148 as an answer, you shaad anrar "Q015". not epa is har e results ar d p ayed below n the table. Use this intcmnston ans er he following uuestions. You should r t our answers n de mal form rounded to the re rest thousand for spamham monay nigeriamcny y proft bankbankhame buy nigeria hme profit check home gera wire Based on tha data above, eatimate the probability af an arbitrary email bang spam, pspam). Based on the data abowa, estimate the probablity af an arbitrary email baing ham, ptham). Part B. Given that you know an email s spam, estmate the probabiity that it ccntains the werd "home Thst is, estimate pthome spam) Elven that you krow an amall s ham, astimato the pratabilty that It cortains tha werd "hama. That a, astmaca p(home ham) Part C. Ae discuesed in dlses, we can cstegarize an emai by comper ng pthan emsil) to p(spam I cmail), and cassify ng the give emsl according to which cuantity s larger. In gereral, these condticral probsblit.es are eetimated ueing Bsyes Rule ss picmail l caleguty)(category) pemail) cntegory email)- We note that both the 8pam and ham oomputatiore, the cer or inator n Campina the astimated numerator ta,spam I hnme). Compute the eetirmated numerator forpham bue 18 fraction ie 89 me and thus we can reteao cl888fy the emai acco oing to whic nn erator is larger. Part D Bssed on your wors above, woud or sparn titer dasrty an emei contanng solely the word-home' as harm or spam? Note: Make sure 1 coun e-check your artseers tcr Part C before mak ng a selection!

Explanation / Answer

Part A
P(spam) = 3/5 = 0.6
P(ham) = 2/5 = 0.4

Part B
P(home and spam) = 1/5 = 0.2
P(home | spam) = P(home and spam)/P(spam) = 0.2/0.6 = 0.3333

P(home and ham) = 2/5 = 0.4
P(home | ham) = P(home and ham)/P(ham) = 0.4/0.4 = 1

Part C
P(home) = 3/5 = 0.6
P(spam | home) = P(home and spam)/P(home) = 0.2/0.6 = 0.333

P(ham | home) = P(ham and home)/P(home) = 0.4/0.6 = 0.6667

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