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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