a genuine riddle

A riddle from The Riddler that was pure (if straightforward) logic rather than brute force compulation or mathematical modelling:

Four bags of many marbles are labelled R(ed), B(lue), G(green) and μ (mixed), except that all labels are wrong. Given the possibility to draw two balls, one at a time, from any bag, is it possible to select two monochromatic bags?

Bag μ draw is returning a color, R say, as it is a monochromatic bag. Drawing from another color bag, B say, will produce R or B, in which case it is μ, i.e., mixed (polychromatic), which means the other bags are monochromatic, or G. For this last case, bag B is either polychromatic, in which case bag G is made of blue marbles and bag R of green marbles, or monochromatic, in which case bag G is mixed and bag R is full of blue marbles, but monochromatic for either situation, hence to be chosen on top of bag μ.

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