An email filter is planned to separate valid emails from spam. The word "free" occurs in 90% of the spam messages and only 5% of the valid messages. Additionally, 40% of the messages are spam. Determine the probability that the message contains "free" given that it is valid (round your answer to 4 decimals).
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The probability of a valid message containing the word "free" is given as 5%. Show more…
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You have 100 emails in your inbox, 60 are spam, and 40 are not. Of the 60 spam emails, 35 contain the word "free". Of the rest, 3 contain the word "free". This information is summarized in the 2x2 contingency table below. Given that an email is spam, determine the probability that it contains the word "free". “free” | No “free” | Total Spam | 35 | 25 | 60 Not spam | 3 | 37 | 40 Total | 38 | 62 | 100
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