Conditional probability and approaching by intuition

[Rajeev Bagra]

A spam filter is designed by looking at commonly occurring phrases in spam. Suppose that 80% of email is spam. In 10% of the spam emails, the phrase “free money” is used, whereas this phrase is only used in 1% of non-spam emails. A new email has just arrived, which does mention “free money”. What is the probability that it is spam?

To build intuition: suppose there were 1000 emails in total. then 800 are spam, and 80 have “free money” in them. 200 weren’t spam and 2 have “free money” in them. Therefore 82 had “free money” in them and 80 of those were spam (https://math.stackexchange.com/q/1942104).

 

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