The grand master

Tordek has mastered the art of fighting. With his powerful broadsword he does 1d10+13 damage with each hit, and gets 3 swings per round.

He is fighting a dragon and needs to inflict 30 or more hit points to slay the beast. If two of his three swings connect, what are his chances of finishing the dragon off?

Details:

1d10+13 means "roll a 10-sided die with faces $$1, 2, \ldots, 10$$, and add 13 to the result". This means the result is picked uniformly randomly from $$14, 15, \dots, 23$$.

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