It is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email?
Answers
Answer:
it is estimated that 50% of emails rae spam
Given : Estimated that 50% of emails are spam emails
A certain brand of software claims that it can detect 99% of spam emails,
the probability for a false positive (a non-spam email detected as spam) is 5%.
To Find : if an email is detected as spam, then what is the probability that it is in fact a non-spam email
Solution:
Let say Total Mails are = 1000X
Spam mails are = (50/100)1000X = 500X
Non Spam Mails are = 1000X- 500X = 500X
can detect 99% of spam emails,
SPAM mails detected which are spam = (99/100)500X = 495X
Spam mails not detected which are spam = 500X - 495X = 5X
false positive (a non-spam email detected as spam) is 5%.
Spam mails detected which are not spam = (5/100) 500X = 25X
Spam mails not detected which are not spam = 500X - 25X = 475
Spam Mails Detected Spam = 495X
Non Spam mails Detected Spam = 25X
Total Mails detected Spams = 495X + 25X = 520X
what is the probability that it is in fact a non-spam email = 25X/520X
= (25/520)
= 5/104
= 0.0481
f an email is detected as spam, then the probability that it is in fact a non-spam email = 0.0481
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