Question

Q.2. A Spam Assassin works by making users train the system. It looks for patterns in the words in emails marked as spam by the user. If emails marked as spam then the word “offer” appears in 15% of the mails. Assuming 0.5% of mail includes the word “offer” if they are non-spam. 50% of all emails received by the user are spam that means rest 50% of emails are non-spam. Find the probability that a mail is a spam given that the word “offer” appears in it.

Answer 1

Answer:

Probability that the mail will be classified as spam = 0.10425

Explanation:

Probability of classifying a spam mail as spam = 0.95

Probability of classfying a mail as a spam when it is not a spam = 0.10

Actual spam mails = 0.5%

Probability of a mail being a spam = 0.5/100 = 0.005

A mail is classified as spam = Mail is a spam and the system classifies it correctly or a mail is not a spam and the system gives false positive

Thus,

Probability that a mail is classified as spam

= Probability that the mail is a spam and the system classifies it as such + Probability that the mail is not a spam and the system gives false positive

= 0.005 × 0.95 + 0.995 × 0.1

= 0.00475 + 0.0995

= 0.10425