An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in $60 \%$ of the spam messages and only $4 \%$ of the valid messages. Also, $20 \%$ of the messages are spam. Determine the following probabilities: a. The message contains free. b. The message is spam given that it contains free. c. The message is valid given that it does not contain free.
Added by Joseph G.
Step 1
20$ - Probability of word "free" occurring in spam messages: $0.60$ - Probability of message being valid: $1 - 0.20 = 0.80$ - Probability of word "free" occurring in valid messages: $0.04$ - Using total probability, the probability of a message containing the word Show more…
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