[All Steps] An email filter is planned to separate valid emails from spam. The word free occurs in 62% of the spam messages and only 5% of the valid messages.
Question: An email filter is planned to separate valid emails from spam. The word free occurs in 62% of the spam messages and only 5% of the valid messages. Furthermore, it is known that 22% of all email messages are spam.
- What is the probability that a randomly selected email is a valid message?
- What is the probability that a randomly selected email contains the word free?
- What is the probability that a randomly selected email is spam given it contains the word free?
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