Don't fret! You don't necessarily mark 10 problems. I've played several games where we sailed through with very few Ship Problems, and in more than half the games, we managed to make it home in one piece. I think it owes a lot to the simple fact that no dice reproduce their odds perfectly: Sometimes, you roll well ... and sometimes you don't.
The Complications cards tip that equation just enough in your favor, especially if you play them strategically. For instance, if you play a card that's tagged with the kind of problem you'd mark next anyway (or with one you've already marked), it doesn't cause problems to snowball.
I encourage you to give it a whirl. You might be surprised!