on a wing and a prayer

(idiom) with only a very small chance of success

Example Sentences:

A: How did you do on your medical school exam?
B: I got 51%
A: Do you think you will get into Harvard?
B: Only on a wing and a prayer.

The inexperienced baseball team was on a wing and a prayer as they prepared to play the defending champions.

From the News:

Finding love on a wing and a prayer

Similar idioms:

1. take someone under one’s wing
2. wing it
3. blessing in disguise