Chromatography
filtration
That would depend on how many yellow and blue marbles are in a pack. If yellow and blue marbles are sold separately and there are the same number of marbles in a pack, buy one of each. That's probably not the case.
In order for 4 red marbles to be one-third of a group and 3 blue marbles to make up one-fourth of the same group the number has to equal 12.
7.5 grams
7
1 in 5.45 of picking at least 2 blue marbles any 2 from 3 is 3 correct picks =3X7(red)=21 of 2 blue only 1 pick of 3 blue only any 3 from 10=120 120/22=5.45
I suppose that the manual separation is the most simple method.
6
That would depend on how many yellow and blue marbles are in a pack. If yellow and blue marbles are sold separately and there are the same number of marbles in a pack, buy one of each. That's probably not the case.
Put them in water.
In order for 4 red marbles to be one-third of a group and 3 blue marbles to make up one-fourth of the same group the number has to equal 12.
There has to be 12 marbles in the group. If 4 are red that is 1/3 of 12 and if 3 are blue that is 1/4 of 12. The rest can be any color. That is how you explain how four red marbles can make up 1/3 of a group of marbles and three blue marbles make up 1/4 of the same group :)
7.5 grams
7
Put them in water.
minus one red marble plus one blue marble
At the simplest level, one would analyze the color of each marble, creating two piles of marbles (one red and one blue). If the person was not able to see colors, they might consider using a spectrometer (spectrograph). Measuring each marble individually, each marble would be placed in the device and the wavelength would be displayed by the device. Based on the wavelength (red is in the range of 620-750nm and blue is in the range of 450-475nm), the person would still create two piles of marbles, the higher wavelength one (indicating red) and the lower wavelength one (indicating blue).
Density is mass per unit volume. More marbles is more mass, but will be more volume as well. If the marbles are all the same, any number of them will have the same density, which is 2.5 grams/cm3. This is a "thinking" problem rather than a "calculation" problem.