off-chance of a maybe

Improbable, or highly unlikely; about as likely as the chance that "maybe" means "yes" rather than "no."; An unbelievable eventuality.

"What, from here? On the off-chance of a maybe that you make this basket, I'll wash BOTH your cars."

Person 1:"Its today? I didn't study!"

Person 2: "Don't worry, you won't fail!"
Person 1 sarcastically: "Sure I won't! On the off-chance of a maybe Mr. Hickerman forgot to bring the exam today!"