Question

If we consider spam email and do a Bayesian analysis the word rolex and find that 50% of spam contains that word but only 1% of non spam contains it then calculate probability of spam if an email contains rolex.

Answer 1

Given ,

P( rolex I spam) = 0.50

P(rolex I non spam) =0.01

To find , P( spam I rolex) =?

Using Bayes' theorem

P( spam I rolex) = P( rolex I spam) *P( spam) / P( rolex)

Now, P(spam) =P(non spam) =0.5 ( we assume that an email being spam or nonspam is equally likely)

P( rolex) = P( rolex I spam ) *P(spam) + P( rolex I non spam ) *P( non spam)

= 0.50 *0.50 + 0.01 *0.50 = 0.255

Therefore ,

P( spam I rolex) = P( rolex I spam) *P( spam) / P( rolex)

= 0.50 *0.50 / 0.255

= 0.9804