Question

A spam filtering system has a probability of 0.95 to classify correctly a mail as spam and 0.10 probability of giving false positives .It is estimated that 0.5% of the mails are actual spam mails​

Answer 1

Answer:

Probability that the mail will be classified as spam = 0.10425

Step-by-step explanation:

The complete question is:

A spam filtering system has a probability of 0.95 to classify correctly as spam and 0.10 probability of giving false positives. It is estimated that 0.5% of the mail are actual spam mails. Suppose that the system is now given a new mail to be classified as spam/not-spam. What is the probability that mail will be classified as spam?

Solution:

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