An email filter is planned to separate valid e-mails from spam. The word free occurs in 72% of the spam messages and only 5% of the valid messages. Also, 13% of the messages are spam. (a) If an email message is randomly selected, find the probability that it is spam, given that it contains the word free. (b) If an email message is randomly selected, find the probability that it is valid, given that it does not contain the word free.