# Choosing Monochromatic Marbles

**Discrete Mathematics**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 \(m+n \)?