Consider the following scenario in email filtering. You know based on your data that 10% of messages sent out are phishing attempts. Now, you look for a few keywords to improve your estimate of whether a particular message is a phishing email. In particular, you see two interesting words in a message you are considering that might indicate that the message is or is not a phishing email. These words and the likelihood that they appear in both a phishing and non-phishing message are listed below. Apply Bayes rule to update the probability that the message is a phishing email once for each word and give the final probability that the message is a phishing email. Note that your prior for the second update is based on the posterior probability after applying Bayes rule for the first word.
Phishing Not Phishing
Urgent 0.15 0.02
Password 0.10 0.01
