Basing itself on the presence of an infinite amount of black and red balls, whether which one would be picked can be calculated through statistics. However, whilst not having a number, it might not be too difficult. Though, as both are infinite, the two pools can be be reduced to simple statistical values. For instance say 100 red / 100 white balls, providing with 2x 100 balls or 200 in this case.
However, while asking this question, it might be more interesting to ask, when picking a defined amount of red balls, what is the chance of a white ball ending up in these red balls, due to the wrong-interval of yourself or the machine that does the sorting for you. Though while we lack several parameters such as size, circumference, surface, volume and related parameters, a good mathematical probability score cannot be created using modernday clustering software.