Question

A special feature on your email app is that it catches spam emails and rejects them before you see them. One of the the things that it looks for is exclamation points--”You’ve won!!! A trip to the Bahamas!!”. The spam filter is about 75% accurate at catching spam. And the rate of emails coming that are spam is 12%. You get sent an email that is identified by the program as spam. What’s the probability that it is spam?

Answer 1

P(catches as spam)= P(spam and catches)+P(not spam and catches) =0.12*0.75+0.88*(1-0.75)

=0.31

therefore P(spam given catches as spam) =P(spam and catches)/P(catches)

=0.12*0.75/0.31 =0.2903