Less than a week after health insurer Anthem warned that a breach of its network exposed the personal information of as many as 80 million people, scammers are sending phishing e-mails that target those unlucky individuals.

The fraudulent e-mails claim they are official Anthem communications being sent to current and former customers. The messages promise free credit monitoring services for people who click on a link that asks for personal data.

"This outreach is from scam artists who are trying to trick consumers into sharing personal data," Anthem officials wrote in an advisory. "There is no indication that the scam e-mail campaigns are being conducted by those that committed the cyber attack, or that the information accessed in the attack is being used by the scammers."

The economics of spam and phishing campaigns allow fraudsters to make a profit even when only a tiny percentage of people take the bait. The e-mails are typically sent from compromised computers, making it virtually free to send an unlimited number of them. With 80 million Anthem customers or employees affected out of a country with a population of 316 million, there's a one-in-four chance that one of the messages will reach someone with good reason to think her data was exposed. If even a small portion of potentially affected people fall for the phishing e-mails, the scammers stand to make money on the campaign.