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 arwe 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?
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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
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