When Will Petr Win?

Petr has ten different two-player board games on his shelf. He has them numbered 1 through 10. When he plays the game $$n$$ against Diego, he has a $$\frac{n^2}{100}$$ chance of winning. If Petr rolls a fair ten-sided die to determine which game to play, the probability that he will win against Diego can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are positive, coprime integers. What is the value of $$a + b$$?

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