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!	.049
Today!	.047
here!	.033
available	.012
fingertips!	.012

Also suppose that the proportions of ham messages that have these words are

Shipping!	.0016
Today!	.0020
here!	.0020
Available!	.0039
Fingertips!	.0009

Round your answers to three decimal places

a. 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?

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?

c. 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?

Answer 1