You can't walk through any good fantasy story without tripping over a prophecy or two. Sybil Trelawney makes one in Harry Potter and the Order of the Phoenix. Eowyn fulfills one in The Return of the King. And there are more prophecies in The Blood of Olympus than you can shake a scepter of Diocletian at. Because it's a story rooted in Greek and Roman myth, the prophecies almost all have a tendency to come true. But since the characters are demigods—and not mere mortal pawns of the gods—they have at least a little agency when it comes to determining their own fate.
Questions About Fate and Free Will
Why does the crew of the Argo II play right into the hands of fate by traveling to the Parthenon, exactly where the bad guys want them?
How do certain characters, like Leo and Percy, play into the fates, while others seem to defy them?