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It's always fun when you fly above the skies in ORAS only to accidently fly into a giant cloud, summoning an unexpected legendary battle. As a joke, I threw a Quick Ball, and..... It caught.

What were the odds of me capturing this legendary in a quick ball with full health?

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I assume you're playing Alpha Sapphire, if not, I'll edit my answer.

You have a 5.24% chance of capturing it per ball. Thus, you have at least a 50% chance of catching it within 13 balls and at least a 95% chance of catching it within 56 balls.

Sources:Catch Calculator, Bulbapedia

I've hoped I've helped!

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To be more specific, what is it's HP IV?
I don't think IVs matter when the Pokemon has full health.