A spam filer is designed by screening commonly occurring phrases in spam. Suppose that 60% of  email is spam. In 20% of the spam emails, the phrase “free gift card” is used. In non-spam emails,  99.5% of them do not mention “free gift card”. What is the probability that a newly arrived email  which does mention “free gift card”, is not spam?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
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A spam filer is designed by screening commonly occurring phrases in spam. Suppose that 60% of 
email is spam. In 20% of the spam emails, the phrase “free gift card” is used. In non-spam emails, 
99.5% of them do not mention “free gift card”. What is the probability that a newly arrived email 
which does mention “free gift card”, is not spam?

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It is given that 60% of email is spam and in 20% of the spam emails, the phrase “free gift card” is used.

99.5% of the non-spam emails do not mention “free gift card”.

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