Appeal to probability:

Mathematical Fallacy
Definition Example
When it is assumed that, because something could happen, it is inevitable that it will happen. I’m certain to win the lottery if I just keep buying tickets.
A remote possibility does not equate to an inevitability over a finite time. You may never win the lottery.

Case Study One

The real possibility that a meteor will strike your house while you sleep does not warrant your concern.

Case Study Two

“I’m going to play professional basketball when I grow up. I don’t need to worry about my grades much since I’ll be making millions after I am drafted into the NBA. I know there are only a couple hundred professional slots, and millions of aspiring young players, but since I have as much a chance as any other young player, I will succeed.”

Keep in mind that a fallacious argument does not entail an erroneous position.

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