Question

11. One way to design a spam filter is to look at the words in an email. In particular, some words are more Trequent in spam emails. Suppose that we have the following 50% of emails are spam 1% of spam emails contain the word "re 001% of non-spam emails contain the word "refinance" Suppose that an email is checked and found to contain the word "refinance". What is the probability that the email is spam?

Answer 1

Bayes' Theorem: P(A | B) = P(A and B)/P(B)

P(spam) = 50% = 0.5

P(word refinance is found | spam) = 1% = 0.01

P(word refinance is found | not spam) = 0.1% = 0.001

(In question, its typed as 001%, but its taken as 0.1%, assuming its a typing error)

P(spam | word refinance is found) = P(spam and word refinance is found) / P(word refinance is found)

= ( P(a mail is spam and word refinance is found)) / (P(a mail is spam and word refinance is found + a mail is not spam and word refinance is found)

= (0.5x0.01)/(0.5x0.01 + 0.5x0.0.001)

= 0.9091