Choosing Monochromatic Marbles

Probability Level 3

There are two boxes which contain both black and white marbles. The total number of marbles in the two boxes is 25. When one marble is taken out of each box randomly, the probability that both marbles are black is $\frac{27}{50}$ ,

When one marble is taken out of each box randomly, the probability that both marbles are white is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?

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