# John's Red and Blue Balls

John has a box that contains one red ball and one blue ball. Every minute he reaches into the box and randomly takes out a ball from it (without looking). No matter which ball he took out, he puts it back ${together\ with}$ another ball of the same color. Thus, after $n$ minutes, the box contains a total of $n+2$ balls.

The probability that after $2$ hours, the box contains exactly $77$ blue balls, can be written as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. Find $a+b$.

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