A spam filter is a computer program that checks each incoming email and tries to

Question

A spam filter is a computer program that checks each incoming email and tries to determine if whether it’s spam or a legitimate email.   If the program thinks the email is spam, it places the email in the spam folder, and the user doesn’t see it unless he/she specifically opens the spam folder. Since about 5% of all emails we receive are spam, this is a great service. The spam filter we have is pretty good. It correctly recognizes spam 98% of the time, and only one time out of a thousand does it incorrectly label a legitimate email as spam. With those statistics, determine what proportion of the emails in the spam folder are actually legitimate emails.

Explanation / Answer

Proportion of mails in spam folder that are actually legitimate = Number of legitimate mails in spam folder / Total number of mails in spam folder

= 0.95x0.001/(0.95x0.001 + 0.05x0.98)

= 0.019

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